97:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Interdisciplinariedad:@0.684804:0.108023:0.831589:0.108023:0.831589:0.092551:0.684804:0.092551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática :@0.685042:0.137073:0.773379:0.137073:0.773379:0.121600:0.685042:0.121600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Medicina:@0.638498:0.152915:0.715295:0.152915:0.715295:0.137442:0.638498:0.137442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En medicina, se :@0.638498:0.168334:0.742367:0.168334:0.742367:0.153271:0.638498:0.153271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
usa un aparato :@0.638498:0.184176:0.738830:0.184176:0.738830:0.169113:0.638498:0.169113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamado litotriptor :@0.638498:0.200018:0.761716:0.200018:0.761716:0.184955:0.638498:0.184955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para desintegrar :@0.638498:0.215860:0.746833:0.215860:0.746833:0.200797:0.638498:0.200797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cálculos renales por :@0.638498:0.231702:0.769489:0.231702:0.769489:0.216639:0.638498:0.216639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medio de ondas acuáticas :@0.638498:0.247544:0.810983:0.247544:0.810983:0.232481:0.638498:0.232481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de choque. El funcionamiento :@0.638498:0.263386:0.837512:0.263386:0.837512:0.248323:0.638498:0.248323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de este aparato se basa en la :@0.638498:0.279228:0.825758:0.279228:0.825758:0.264165:0.638498:0.264165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiente forma: se coloca un :@0.638498:0.295070:0.830226:0.295070:0.830226:0.280007:0.638498:0.280007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aparato en forma de elipsoide :@0.638498:0.310912:0.835661:0.310912:0.835661:0.295849:0.638498:0.295849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lleno de agua pegado al cuerpo :@0.638498:0.326754:0.845602:0.326754:0.845602:0.311691:0.638498:0.311691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del paciente y en la parte del :@0.638498:0.342596:0.827763:0.342596:0.827763:0.327533:0.638498:0.327533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
foco se generan ondas; el foco :@0.638498:0.358438:0.837246:0.358438:0.837246:0.343375:0.638498:0.343375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la otra parte del elipsoide :@0.638498:0.374280:0.826128:0.374280:0.826128:0.359217:0.638498:0.359217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se coloca en los cálculos del :@0.638498:0.390122:0.822926:0.390122:0.822926:0.375059:0.638498:0.375059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
paciente.:@0.638498:0.405964:0.696686:0.405964:0.696686:0.390901:0.638498:0.390901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Adaptado de: http://www.academia.:@0.639266:0.427105:0.846236:0.427105:0.846236:0.413476:0.639266:0.413476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
edu/18354808/Aplicacion_de_la_:@0.652745:0.441438:0.846236:0.441438:0.846236:0.427809:0.652745:0.427809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elipse_a_la_Ingenieria:@0.721481:0.455771:0.846236:0.455771:0.846236:0.442142:0.721481:0.442142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga:@0.638503:0.488198:0.686135:0.488198:0.686135:0.472726:0.638503:0.472726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 sobre las aplicaciones :@0.686135:0.487776:0.832430:0.487776:0.832430:0.472712:0.686135:0.472712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la hipérbola y :@0.638503:0.503618:0.749882:0.503618:0.749882:0.488554:0.638503:0.488554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
confecciona:@0.749882:0.504040:0.834331:0.504040:0.834331:0.488568:0.749882:0.488568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.834333:0.503618:0.838115:0.503618:0.838115:0.488554:0.834333:0.488554:0.000000
un resumen en el cuaderno.:@0.638503:0.519460:0.818500:0.519460:0.818500:0.504396:0.638503:0.504396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos la ecuación: ( ,  )    , tal que:@0.108233:0.096194:0.432430:0.096194:0.432430:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.307183:0.096310:0.329242:0.096310:0.329242:0.079841:0.307183:0.079841:0.000000:0.000000:0.000000
:@0.339336:0.095676:0.353988:0.095676:0.353988:0.082302:0.339336:0.082302:0.000000
:@0.358130:0.095107:0.371435:0.095107:0.371435:0.082245:0.358130:0.082245:0.000000
2:@0.371433:0.089842:0.376386:0.089842:0.376386:0.080224:0.371433:0.080224:0.000000
|:@0.108233:0.121411:0.113242:0.121411:0.113242:0.101614:0.108233:0.101614:0.000000
   (  +  )  +   –   (  –  )  + :@0.113242:0.120674:0.304471:0.120674:0.304471:0.104176:0.113242:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.131621:0.120790:0.165374:0.120790:0.165374:0.104321:0.131621:0.104321:0.000000:0.000000:0.000000
2:@0.171326:0.114321:0.176279:0.114321:0.176279:0.104703:0.171326:0.104703:0.000000
y:@0.195370:0.120790:0.203057:0.120790:0.203057:0.104321:0.195370:0.104321:0.000000
2:@0.203057:0.114321:0.208010:0.114321:0.208010:0.104703:0.203057:0.104703:0.000000
x c:@0.241031:0.120790:0.274475:0.120790:0.274475:0.104321:0.241031:0.104321:0.000000:0.000000:0.000000
2:@0.280426:0.114321:0.285379:0.114321:0.285379:0.104703:0.280426:0.104703:0.000000
y:@0.304471:0.120790:0.312158:0.120790:0.312158:0.104321:0.304471:0.104321:0.000000
2 :@0.312157:0.114321:0.319525:0.114321:0.319525:0.104703:0.312157:0.104703:0.000000:0.000000
|:@0.320087:0.121411:0.325096:0.121411:0.325096:0.101614:0.320087:0.101614:0.000000
 = 2 De la definición de valor:@0.325096:0.120674:0.541460:0.120674:0.541460:0.104176:0.325096:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.352684:0.120790:0.368347:0.120790:0.368347:0.104321:0.352684:0.104321:0.000000:0.000000:0.000000
absoluto, se deduce    (  +  )  +   –   (  –  )  +   = ±2  y de esta, :@0.108227:0.145153:0.581164:0.145152:0.581164:0.128655:0.108227:0.128655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.271460:0.145269:0.305212:0.145269:0.305212:0.128800:0.271460:0.128800:0.000000:0.000000:0.000000
2:@0.311168:0.138800:0.316121:0.138800:0.316121:0.129182:0.311168:0.129182:0.000000
y:@0.335214:0.145268:0.342901:0.145268:0.342901:0.128799:0.335214:0.128799:0.000000
2:@0.342899:0.138800:0.347852:0.138800:0.347852:0.129182:0.342899:0.129182:0.000000
x c:@0.380873:0.145268:0.414318:0.145268:0.414318:0.128799:0.380873:0.128799:0.000000:0.000000:0.000000
2:@0.420270:0.138800:0.425223:0.138800:0.425223:0.129182:0.420270:0.129182:0.000000
y:@0.444314:0.145268:0.452001:0.145268:0.452001:0.128799:0.444314:0.128799:0.000000
2 :@0.452001:0.138800:0.459369:0.138800:0.459369:0.129182:0.452001:0.129182:0.000000:0.000000
a:@0.498325:0.145268:0.507303:0.145268:0.507303:0.128799:0.498325:0.128799:0.000000
consideremos la ecuación::@0.108242:0.162503:0.293880:0.162503:0.293880:0.146005:0.108242:0.146005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )     tal que    (  +  )  +   –   (  –  )  +   = ±2 .:@0.108242:0.186982:0.497792:0.186981:0.497792:0.170484:0.108242:0.170484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.114195:0.187098:0.136254:0.187098:0.136254:0.170629:0.114195:0.170629:0.000000:0.000000:0.000000
:@0.146338:0.186463:0.160991:0.186463:0.160991:0.173089:0.146338:0.173089:0.000000
:@0.165133:0.185894:0.178437:0.185894:0.178437:0.173032:0.165133:0.173032:0.000000
2:@0.178437:0.180630:0.183391:0.180630:0.183391:0.171012:0.178437:0.171012:0.000000
x c:@0.259200:0.187097:0.292953:0.187097:0.292953:0.170628:0.259200:0.170628:0.000000:0.000000:0.000000
2:@0.298902:0.180630:0.303855:0.180630:0.303855:0.171012:0.298902:0.171012:0.000000
y:@0.322948:0.187097:0.330635:0.187097:0.330635:0.170628:0.322948:0.170628:0.000000
2:@0.330633:0.180630:0.335586:0.180630:0.335586:0.171012:0.330633:0.171012:0.000000
x c:@0.368607:0.187097:0.402052:0.187097:0.402052:0.170628:0.368607:0.170628:0.000000:0.000000:0.000000
2:@0.408004:0.180630:0.412957:0.180630:0.412957:0.171012:0.408004:0.171012:0.000000
y:@0.432048:0.187097:0.439735:0.187097:0.439735:0.170628:0.432048:0.170628:0.000000
2 :@0.439735:0.180630:0.447103:0.180630:0.447103:0.171012:0.439735:0.171012:0.000000:0.000000
a:@0.486059:0.187097:0.495037:0.187097:0.495037:0.170628:0.486059:0.170628:0.000000
Resulta   (  +  )  +    = –2  +   (  –  )  +  . Elevando ambos miem-:@0.108229:0.221683:0.595251:0.221683:0.595251:0.205185:0.108229:0.205185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.179067:0.221799:0.212820:0.221799:0.212820:0.205330:0.179067:0.205330:0.000000:0.000000:0.000000
2:@0.218775:0.215331:0.223729:0.215331:0.223729:0.205713:0.218775:0.205713:0.000000
y:@0.242819:0.221799:0.250506:0.221799:0.250506:0.205330:0.242819:0.205330:0.000000
2:@0.250506:0.215331:0.255459:0.215331:0.255459:0.205713:0.250506:0.205713:0.000000
a:@0.297689:0.221799:0.306667:0.221799:0.306667:0.205330:0.297689:0.205330:0.000000
x c:@0.339996:0.221799:0.373440:0.221799:0.373440:0.205330:0.339996:0.205330:0.000000:0.000000:0.000000
2:@0.379391:0.215331:0.384344:0.215331:0.384344:0.205713:0.379391:0.205713:0.000000
y:@0.403435:0.221799:0.411121:0.221799:0.411121:0.205330:0.403435:0.205330:0.000000
2 :@0.411121:0.215331:0.418489:0.215331:0.418489:0.205713:0.411121:0.205713:0.000000:0.000000
bros al cuadrado, se obtiene: :@0.108229:0.239034:0.313650:0.239034:0.313650:0.222536:0.108229:0.222536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  )  +   =  –2  +   (  –  )  +     , donde: :@0.108229:0.263513:0.427276:0.263513:0.427276:0.247016:0.108229:0.247015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.114182:0.263628:0.147935:0.263628:0.147935:0.247160:0.114182:0.247160:0.000000:0.000000:0.000000
2:@0.153890:0.257160:0.158843:0.257160:0.158843:0.247542:0.153890:0.247542:0.000000
y:@0.177936:0.263629:0.185622:0.263629:0.185622:0.247160:0.177936:0.247160:0.000000
2:@0.185622:0.257160:0.190576:0.257160:0.190576:0.247542:0.185622:0.247542:0.000000
a:@0.232804:0.263629:0.241781:0.263629:0.241781:0.247160:0.232804:0.247160:0.000000
x c:@0.275110:0.263629:0.308555:0.263629:0.308555:0.247160:0.275110:0.247160:0.000000:0.000000:0.000000
2:@0.314505:0.257160:0.319458:0.257160:0.319458:0.247542:0.314505:0.247542:0.000000
y:@0.338551:0.263629:0.346238:0.263629:0.346238:0.247160:0.338551:0.247160:0.000000
2  2:@0.346236:0.257160:0.365740:0.254702:0.365740:0.245084:0.346236:0.247542:0.000000:0.000000:0.000000:0.000000
x:@0.108226:0.288108:0.115701:0.288108:0.115701:0.271639:0.108226:0.271639:0.000000
2:@0.115708:0.281639:0.120661:0.281639:0.120661:0.272021:0.115708:0.272021:0.000000
 + 2  +   +    = 4 – 4:@0.120662:0.287992:0.298810:0.287992:0.298810:0.271494:0.120662:0.271494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cx c:@0.148250:0.288107:0.189188:0.288107:0.189188:0.271639:0.148250:0.271639:0.000000:0.000000:0.000000:0.000000
2:@0.189186:0.281639:0.194139:0.281639:0.194139:0.272021:0.189186:0.272021:0.000000
y:@0.213231:0.288107:0.220918:0.288107:0.220918:0.271639:0.213231:0.271639:0.000000
2:@0.220916:0.281639:0.225870:0.281639:0.225870:0.272021:0.220916:0.272021:0.000000
a  :@0.257600:0.288107:0.275672:0.288107:0.275672:0.271639:0.257600:0.271639:0.000000:0.000000:0.000000
2:@0.266577:0.281639:0.271530:0.281639:0.271530:0.272021:0.266577:0.272021:0.000000
a    x c:@0.298810:0.288107:0.359611:0.288107:0.359611:0.271639:0.298810:0.271639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  –  )  +   + (  –  )  + :@0.320214:0.287992:0.490731:0.287992:0.490731:0.271494:0.320214:0.271494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.365562:0.281639:0.370515:0.281639:0.370515:0.272021:0.365562:0.272021:0.000000
y:@0.389607:0.288107:0.397294:0.288107:0.397294:0.271639:0.389607:0.271639:0.000000
2:@0.397292:0.281639:0.402245:0.281639:0.402245:0.272021:0.397292:0.272021:0.000000
x c:@0.427291:0.288107:0.460735:0.288107:0.460735:0.271639:0.427291:0.271639:0.000000:0.000000:0.000000
2:@0.466686:0.281639:0.471639:0.281639:0.471639:0.272021:0.466686:0.272021:0.000000
y:@0.490731:0.288107:0.498418:0.288107:0.498418:0.271639:0.490731:0.271639:0.000000
2:@0.498418:0.281639:0.503371:0.281639:0.503371:0.272021:0.498418:0.272021:0.000000
= 4 – 4:@0.108233:0.312470:0.172889:0.312470:0.172889:0.295972:0.108233:0.295972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a  :@0.131679:0.312586:0.149751:0.312586:0.149751:0.296117:0.131679:0.296117:0.000000:0.000000:0.000000
2:@0.140656:0.306118:0.145609:0.306118:0.145609:0.296500:0.140656:0.296500:0.000000
a    x c:@0.172889:0.312586:0.233690:0.312586:0.233690:0.296117:0.172889:0.296117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  –  )  +   +   – 2  +   +  .:@0.194293:0.312470:0.415500:0.312470:0.415500:0.295972:0.194293:0.295972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.239641:0.306118:0.244594:0.306118:0.244594:0.296500:0.239641:0.296500:0.000000
y:@0.263686:0.312586:0.271373:0.312586:0.271373:0.296117:0.263686:0.296117:0.000000
2:@0.271371:0.306118:0.276324:0.306118:0.276324:0.296500:0.271371:0.296500:0.000000
x:@0.295417:0.312586:0.302892:0.312586:0.302892:0.296117:0.295417:0.296117:0.000000
2:@0.302891:0.306118:0.307844:0.306118:0.307844:0.296500:0.302891:0.296500:0.000000
cx c:@0.335124:0.312586:0.376063:0.312586:0.376063:0.296117:0.335124:0.296117:0.000000:0.000000:0.000000:0.000000
2:@0.376060:0.306118:0.381014:0.306118:0.381014:0.296500:0.376060:0.296500:0.000000
y:@0.400106:0.312586:0.407793:0.312586:0.407793:0.296117:0.400106:0.296117:0.000000
2:@0.407793:0.306118:0.412746:0.306118:0.412746:0.296500:0.407793:0.296500:0.000000
Aplicando la ley cancelativa (cancelando   +   +  ), se obtiene: :@0.108238:0.347172:0.568863:0.347172:0.568863:0.330674:0.108238:0.330674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.400432:0.347287:0.407907:0.347287:0.407907:0.330819:0.400432:0.330819:0.000000
2:@0.407900:0.340820:0.412853:0.340820:0.412853:0.331202:0.407900:0.331202:0.000000
c:@0.431945:0.347287:0.439131:0.347287:0.439131:0.330819:0.431945:0.330819:0.000000
2:@0.439131:0.340820:0.444085:0.340820:0.444085:0.331202:0.439131:0.331202:0.000000
y:@0.463175:0.347287:0.470862:0.347287:0.470862:0.330819:0.463175:0.330819:0.000000
2:@0.470862:0.340820:0.475815:0.340820:0.475815:0.331202:0.470862:0.331202:0.000000
2  = 4 – 4:@0.108233:0.381873:0.200187:0.381873:0.200187:0.365375:0.108233:0.365375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cx:@0.116729:0.381989:0.131390:0.381989:0.131390:0.365520:0.116729:0.365520:0.000000:0.000000
a  :@0.158978:0.381989:0.177049:0.381989:0.177049:0.365520:0.158978:0.365520:0.000000:0.000000:0.000000
2:@0.167954:0.375521:0.172907:0.375521:0.172907:0.365903:0.167954:0.365903:0.000000
a    x c:@0.200187:0.381989:0.260988:0.381989:0.260988:0.365520:0.200187:0.365520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  –  )  +   – 2:@0.221591:0.381873:0.330903:0.381873:0.330903:0.365375:0.221591:0.365375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.266939:0.375521:0.271892:0.375521:0.271892:0.365903:0.266939:0.365903:0.000000
y:@0.290984:0.381989:0.298671:0.381989:0.298671:0.365520:0.290984:0.365520:0.000000
2:@0.298669:0.375521:0.303622:0.375521:0.303622:0.365903:0.298669:0.365903:0.000000
cx:@0.330903:0.381989:0.345563:0.381989:0.345563:0.365520:0.330903:0.365520:0.000000:0.000000
y de esta última igualdad se deducen las siguientes::@0.108235:0.416575:0.469358:0.416575:0.469358:0.400077:0.108235:0.400077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.108235:0.451276:0.116731:0.451276:0.116731:0.434778:0.108235:0.434778:0.000000
a    x c:@0.116731:0.451392:0.177532:0.451392:0.177532:0.434923:0.116731:0.434923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  –  )  +   = 4 – 4:@0.138134:0.451276:0.288963:0.451276:0.288963:0.434778:0.138134:0.434778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.183481:0.444924:0.188435:0.444924:0.188435:0.435306:0.183481:0.435306:0.000000
y:@0.207527:0.451392:0.215214:0.451392:0.215214:0.434923:0.207527:0.434923:0.000000
2:@0.215212:0.444924:0.220165:0.444924:0.220165:0.435306:0.215212:0.435306:0.000000
a  :@0.247754:0.451392:0.265825:0.451392:0.265825:0.434923:0.247754:0.434923:0.000000:0.000000:0.000000
2:@0.256731:0.444924:0.261685:0.444924:0.261685:0.435306:0.256731:0.435306:0.000000
cx, :@0.288963:0.451392:0.310732:0.451392:0.310732:0.434923:0.288963:0.434923:0.000000:0.000000:0.000000:0.000000
(  –  )  +   =  –       .:@0.349476:0.451276:0.509294:0.451276:0.509294:0.434778:0.349476:0.434778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.355429:0.451392:0.388873:0.451392:0.388873:0.434923:0.355429:0.434923:0.000000:0.000000:0.000000
2:@0.394816:0.444924:0.399769:0.444924:0.399769:0.435306:0.394816:0.435306:0.000000
y:@0.418862:0.451392:0.426549:0.451392:0.426549:0.434923:0.418862:0.434923:0.000000
2:@0.426549:0.444924:0.431502:0.444924:0.431502:0.435306:0.426549:0.435306:0.000000
a :@0.450593:0.451392:0.463712:0.451392:0.463712:0.434923:0.450593:0.434923:0.000000:0.000000
x:@0.499064:0.451392:0.506539:0.451392:0.506539:0.434923:0.499064:0.434923:0.000000
Nuevamente, elevando al cuadrado ambos miembros en la última :@0.108230:0.485978:0.599916:0.485978:0.599916:0.469480:0.108230:0.469480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
igualdad, se tiene::@0.108230:0.503328:0.232664:0.503328:0.232664:0.486831:0.108230:0.486831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  –  )  +   =    –     :@0.263797:0.527807:0.417543:0.527808:0.417543:0.511310:0.263797:0.511310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x c:@0.269750:0.527923:0.303194:0.527923:0.303194:0.511454:0.269750:0.511454:0.000000:0.000000:0.000000
2:@0.309153:0.521455:0.314106:0.521455:0.314106:0.511837:0.309153:0.511837:0.000000
y:@0.333198:0.527924:0.340885:0.527924:0.340885:0.511455:0.333198:0.511455:0.000000
2:@0.340884:0.521455:0.345837:0.521455:0.345837:0.511837:0.340884:0.511837:0.000000
a :@0.373213:0.527924:0.386333:0.527924:0.386333:0.511455:0.373213:0.511455:0.000000:0.000000
x   :@0.417543:0.527924:0.437444:0.527924:0.437444:0.511455:0.417543:0.511455:0.000000:0.000000:0.000000:0.000000
,:@0.437444:0.527808:0.440199:0.527808:0.440199:0.511310:0.437444:0.511310:0.000000
y de esta se deducen las siguientes::@0.108239:0.557984:0.354773:0.557984:0.354773:0.541486:0.108239:0.541486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.108239:0.582579:0.115714:0.582579:0.115714:0.566110:0.108239:0.566110:0.000000
2:@0.115708:0.576109:0.120661:0.576109:0.120661:0.566491:0.115708:0.566491:0.000000
 – 2  +   +    =   – 2  +       :@0.120660:0.582462:0.348610:0.582462:0.348610:0.565964:0.120660:0.565964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cx c:@0.147940:0.582577:0.188878:0.582577:0.188878:0.566109:0.147940:0.566109:0.000000:0.000000:0.000000:0.000000
2:@0.188877:0.576109:0.193831:0.576109:0.193831:0.566491:0.188877:0.566491:0.000000
y:@0.212923:0.582577:0.220610:0.582577:0.220610:0.566109:0.212923:0.566109:0.000000
2:@0.220608:0.576109:0.225561:0.576109:0.225561:0.566491:0.220608:0.566491:0.000000
a:@0.248796:0.582577:0.257773:0.582577:0.257773:0.566109:0.248796:0.566109:0.000000
2:@0.257773:0.576109:0.262727:0.576109:0.262727:0.566491:0.257773:0.566491:0.000000
cx:@0.290005:0.582577:0.304666:0.582577:0.304666:0.566109:0.290005:0.566109:0.000000:0.000000
x ,:@0.348610:0.582577:0.363888:0.582577:0.363888:0.566109:0.348610:0.566109:0.000000:0.000000:0.000000
2:@0.356083:0.576109:0.361036:0.576109:0.361036:0.566491:0.356083:0.566491:0.000000
x:@0.108238:0.617279:0.115713:0.617279:0.115713:0.600810:0.108238:0.600810:0.000000
2:@0.115708:0.610810:0.120661:0.610810:0.120661:0.601192:0.115708:0.601192:0.000000
 –         +    =   – :@0.120660:0.617163:0.264403:0.617163:0.264403:0.600665:0.120660:0.600665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.164296:0.617279:0.171771:0.617279:0.171771:0.600810:0.164296:0.600810:0.000000
2:@0.171770:0.610810:0.176723:0.610810:0.176723:0.601192:0.171770:0.601192:0.000000
y:@0.195815:0.617279:0.203502:0.617279:0.203502:0.600810:0.195815:0.600810:0.000000
2:@0.203502:0.610810:0.208455:0.610810:0.208455:0.601192:0.203502:0.601192:0.000000
a:@0.231688:0.617279:0.240666:0.617279:0.240666:0.600810:0.231688:0.600810:0.000000
2:@0.240666:0.610810:0.245619:0.610810:0.245619:0.601192:0.240666:0.601192:0.000000
c , :@0.264403:0.617279:0.283534:0.617279:0.283534:0.600810:0.264403:0.600810:0.000000:0.000000:0.000000:0.000000
2:@0.271587:0.610810:0.276541:0.610810:0.276541:0.601192:0.271587:0.601192:0.000000
              x:@0.336166:0.617279:0.401630:0.617279:0.401630:0.600810:0.336166:0.600810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.401633:0.610810:0.406586:0.610810:0.406586:0.601192:0.401633:0.601192:0.000000
 –    =   – :@0.406587:0.617163:0.492165:0.617163:0.492165:0.600665:0.406587:0.600665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.425370:0.617279:0.433057:0.617279:0.433057:0.600810:0.425370:0.600810:0.000000
2:@0.433057:0.610810:0.438010:0.610810:0.438010:0.601192:0.433057:0.601192:0.000000
c:@0.461243:0.617279:0.468429:0.617279:0.468429:0.600810:0.461243:0.600810:0.000000
2:@0.468428:0.610810:0.473381:0.610810:0.473381:0.601192:0.468428:0.601192:0.000000
a .:@0.492165:0.617279:0.508947:0.617279:0.508947:0.600810:0.492165:0.600810:0.000000:0.000000:0.000000
2:@0.501142:0.610810:0.506095:0.610810:0.506095:0.601192:0.501142:0.601192:0.000000
Sea   =   –   > 0. Multiplicando por        la igualdad anterior,:@0.108230:0.651865:0.551162:0.651865:0.551162:0.635367:0.108230:0.635367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.136492:0.651980:0.145758:0.651980:0.145758:0.635512:0.136492:0.635512:0.000000
2:@0.145762:0.645512:0.150715:0.645512:0.150715:0.635894:0.145762:0.635894:0.000000
c:@0.169806:0.651980:0.176992:0.651980:0.176992:0.635512:0.169806:0.635512:0.000000
2:@0.176992:0.645512:0.181945:0.645512:0.181945:0.635894:0.176992:0.635894:0.000000
a:@0.200729:0.651980:0.209707:0.651980:0.209707:0.635512:0.200729:0.635512:0.000000
2:@0.209706:0.645512:0.214659:0.645512:0.214659:0.635894:0.209706:0.635894:0.000000
se obtiene la ecuación ( ,  )     tal que          –         = 1,:@0.108236:0.679901:0.513787:0.679908:0.513787:0.663410:0.108236:0.663403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.275900:0.680016:0.297959:0.680016:0.297959:0.663548:0.275900:0.663548:0.000000:0.000000:0.000000
:@0.308049:0.679389:0.322701:0.679389:0.322701:0.666016:0.308049:0.666016:0.000000
:@0.326842:0.678821:0.340147:0.678821:0.340147:0.665958:0.326842:0.665958:0.000000
2:@0.340147:0.673554:0.345100:0.673554:0.345100:0.663936:0.340147:0.663936:0.000000
a la cual se le conoce como ecuación cartesiana de la hipérbola con :@0.108234:0.714609:0.599914:0.714609:0.599914:0.698111:0.108234:0.698111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eje   como eje principal.:@0.108234:0.731960:0.281061:0.731960:0.281061:0.715462:0.108234:0.715462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.132277:0.732075:0.142237:0.732075:0.142237:0.715607:0.132277:0.715607:0.000000
Si se considera la ecuación::@0.108234:0.766661:0.298128:0.766661:0.298128:0.750164:0.108234:0.750164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )    , tal que     (  +  )  +   –   (  –  )  +   = 2:@0.162003:0.791140:0.533025:0.791140:0.533025:0.774642:0.162003:0.774643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.167956:0.791256:0.190015:0.791256:0.190015:0.774787:0.167956:0.774787:0.000000:0.000000:0.000000
:@0.200105:0.790621:0.214757:0.790621:0.214757:0.777248:0.200105:0.777248:0.000000
:@0.218899:0.790053:0.232204:0.790053:0.232204:0.777191:0.218899:0.777191:0.000000
2:@0.232202:0.784788:0.237156:0.784788:0.237156:0.775170:0.232202:0.775170:0.000000
x c:@0.316970:0.791255:0.350723:0.791255:0.350723:0.774787:0.316970:0.774787:0.000000:0.000000:0.000000
2:@0.356674:0.784788:0.361628:0.784788:0.361628:0.775170:0.356674:0.775170:0.000000
y:@0.380720:0.791255:0.388407:0.791255:0.388407:0.774787:0.380720:0.774787:0.000000
2:@0.388407:0.784788:0.393360:0.784788:0.393360:0.775170:0.388407:0.775170:0.000000
x c:@0.426379:0.791255:0.459824:0.791255:0.459824:0.774787:0.426379:0.774787:0.000000:0.000000:0.000000
2:@0.465776:0.784788:0.470729:0.784788:0.470729:0.775170:0.465776:0.775170:0.000000
y:@0.489822:0.791255:0.497508:0.791255:0.497508:0.774787:0.489822:0.774787:0.000000
2 :@0.497507:0.784788:0.504875:0.784788:0.504875:0.775170:0.497507:0.775170:0.000000:0.000000
a:@0.533025:0.791255:0.542003:0.791255:0.542003:0.774787:0.533025:0.774787:0.000000
y procediendo como en el caso previo, se obtiene la ecuación::@0.108226:0.815619:0.547122:0.815619:0.547122:0.799121:0.108226:0.799121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )     tal que          –          = 1,:@0.227998:0.840098:0.475994:0.840098:0.475994:0.823600:0.227998:0.823600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.233951:0.840213:0.256010:0.840213:0.256010:0.823745:0.233951:0.823745:0.000000:0.000000:0.000000
:@0.266114:0.839579:0.280767:0.839579:0.280767:0.826206:0.266114:0.826206:0.000000
:@0.284909:0.839011:0.298214:0.839011:0.298214:0.826149:0.284909:0.826149:0.000000
2:@0.298214:0.833745:0.303167:0.833745:0.303167:0.824127:0.298214:0.824127:0.000000
que es exactamente la misma obtenida anteriormente. De estos resul-:@0.108240:0.864577:0.595705:0.864577:0.595705:0.848079:0.108240:0.848079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tados, el conjunto  (0,  ,  ) se escribe como::@0.108240:0.881927:0.429977:0.881927:0.429977:0.865429:0.108240:0.865430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.240582:0.889001:0.256993:0.889001:0.256993:0.870865:0.240582:0.870865:0.000000
:@0.264220:0.879903:0.270636:0.879903:0.270636:0.864085:0.264220:0.864085:0.000000
a b:@0.277436:0.882043:0.302578:0.882043:0.302578:0.865574:0.277436:0.865574:0.000000:0.000000:0.000000
ℋ:@0.108233:0.923702:0.124644:0.923702:0.124644:0.905567:0.108233:0.905567:0.000000
(0,  ,  ) =   ( ,  )     |         –         = 1  ,:@0.124647:0.916628:0.407404:0.916628:0.407404:0.900131:0.124647:0.900131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.131872:0.914604:0.138287:0.914604:0.138287:0.898786:0.131872:0.898786:0.000000
a b:@0.145087:0.916744:0.170229:0.916744:0.170229:0.900275:0.145087:0.900275:0.000000:0.000000:0.000000
x y:@0.209511:0.916744:0.231569:0.916744:0.231569:0.900275:0.209511:0.900275:0.000000:0.000000:0.000000
:@0.241661:0.916110:0.256313:0.916110:0.256313:0.902736:0.241661:0.902736:0.000000
:@0.260454:0.915541:0.273758:0.915541:0.273758:0.902679:0.260454:0.902679:0.000000
2:@0.273758:0.910275:0.278712:0.910275:0.278712:0.900657:0.273758:0.900657:0.000000
donde 0 <   <    y   =   –  .:@0.108234:0.949060:0.323273:0.949067:0.323273:0.932569:0.108234:0.932562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a c:@0.186855:0.949175:0.222111:0.949175:0.222111:0.932707:0.186855:0.932707:0.000000:0.000000:0.000000
b:@0.242359:0.949175:0.251625:0.949175:0.251625:0.932707:0.242359:0.932707:0.000000
2:@0.251622:0.942714:0.256575:0.942714:0.256575:0.933096:0.251622:0.933096:0.000000
c:@0.275666:0.949182:0.282852:0.949182:0.282852:0.932714:0.275666:0.932714:0.000000
2:@0.282852:0.942714:0.287805:0.942714:0.287805:0.933096:0.282852:0.933096:0.000000
a:@0.306587:0.949182:0.315565:0.949182:0.315565:0.932714:0.306587:0.932714:0.000000
2:@0.315566:0.942714:0.320519:0.942714:0.320519:0.933096:0.315566:0.933096:0.000000
c:@0.484527:0.443931:0.491713:0.443931:0.491713:0.427462:0.484527:0.427462:0.000000
a:@0.483641:0.460270:0.492618:0.460270:0.492618:0.443801:0.483641:0.443801:0.000000
c:@0.404102:0.520426:0.411288:0.520426:0.411288:0.503958:0.404102:0.503958:0.000000
a:@0.403216:0.536765:0.412194:0.536765:0.412194:0.520296:0.403216:0.520296:0.000000
c:@0.327911:0.574907:0.335097:0.574907:0.335097:0.558438:0.327911:0.558438:0.000000
2:@0.335096:0.568439:0.340049:0.568439:0.340049:0.558821:0.335096:0.558821:0.000000
a:@0.327014:0.591251:0.335992:0.591251:0.335992:0.574783:0.327014:0.574783:0.000000
2:@0.335992:0.584784:0.340945:0.584784:0.340945:0.575166:0.335992:0.575166:0.000000
1:@0.393166:0.644655:0.401662:0.644655:0.401662:0.628158:0.393166:0.628158:0.000000
b:@0.390296:0.661110:0.399562:0.661110:0.399562:0.644641:0.390296:0.644641:0.000000
2:@0.399571:0.654647:0.404524:0.654647:0.404524:0.645029:0.399571:0.645029:0.000000
c:@0.143951:0.609577:0.151137:0.609577:0.151137:0.593108:0.143951:0.593108:0.000000
2:@0.151136:0.603108:0.156089:0.603108:0.156089:0.593490:0.151136:0.593490:0.000000
a:@0.143055:0.625922:0.152032:0.625922:0.152032:0.609453:0.143055:0.609453:0.000000
2:@0.152032:0.619453:0.156985:0.619453:0.156985:0.609835:0.152032:0.609835:0.000000
c:@0.334823:0.609577:0.342009:0.609577:0.342009:0.593108:0.334823:0.593108:0.000000
2:@0.342008:0.603108:0.346961:0.603108:0.346961:0.593490:0.342008:0.593490:0.000000
 – :@0.346961:0.609461:0.365745:0.609461:0.365745:0.592963:0.346961:0.592963:0.000000:0.000000:0.000000
a:@0.365745:0.609577:0.374723:0.609577:0.374723:0.593108:0.365745:0.593108:0.000000
2:@0.374722:0.603108:0.379675:0.603108:0.379675:0.593490:0.374722:0.593490:0.000000
a:@0.350283:0.625922:0.359261:0.625922:0.359261:0.609453:0.350283:0.609453:0.000000
2:@0.359261:0.619453:0.364214:0.619453:0.364214:0.609835:0.359261:0.609835:0.000000
2:@0.430678:0.514612:0.435631:0.514612:0.435631:0.504993:0.430678:0.504993:0.000000
x:@0.416745:0.671960:0.424220:0.671960:0.424220:0.655491:0.416745:0.655491:0.000000
a:@0.415994:0.688299:0.424971:0.688299:0.424971:0.671830:0.415994:0.671830:0.000000
y:@0.466897:0.671960:0.474584:0.671960:0.474584:0.655491:0.466897:0.655491:0.000000
b:@0.466107:0.688299:0.475374:0.688299:0.475374:0.671830:0.466107:0.671830:0.000000
2:@0.432853:0.665975:0.437806:0.665975:0.437806:0.656357:0.432853:0.656357:0.000000
2:@0.483114:0.665975:0.488067:0.665975:0.488067:0.656357:0.483114:0.656357:0.000000
x:@0.373209:0.832968:0.380684:0.832968:0.380684:0.816499:0.373209:0.816499:0.000000
a:@0.372458:0.849306:0.381435:0.849306:0.381435:0.832837:0.372458:0.832837:0.000000
x:@0.301149:0.909307:0.308624:0.909307:0.308624:0.892838:0.301149:0.892838:0.000000
a:@0.300397:0.925646:0.309375:0.925646:0.309375:0.909177:0.300397:0.909177:0.000000
y:@0.423361:0.832968:0.431048:0.832968:0.431048:0.816499:0.423361:0.816499:0.000000
b:@0.422571:0.849306:0.431837:0.849306:0.431837:0.832837:0.422571:0.832837:0.000000
y:@0.351299:0.909307:0.358985:0.909307:0.358985:0.892838:0.351299:0.892838:0.000000
b:@0.350509:0.925646:0.359775:0.925646:0.359775:0.909177:0.350509:0.909177:0.000000
2:@0.389316:0.826983:0.394270:0.826983:0.394270:0.817365:0.389316:0.817365:0.000000
2:@0.317254:0.903321:0.322207:0.903321:0.322207:0.893703:0.317254:0.893703:0.000000
2:@0.439578:0.826983:0.444531:0.826983:0.444531:0.817365:0.439578:0.817365:0.000000
2:@0.367516:0.903321:0.372469:0.903321:0.372469:0.893703:0.367516:0.893703:0.000000
Shutterstock, 585028462:@0.871305:0.314266:0.871305:0.246093:0.859836:0.246093:0.859836:0.314266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los puntos   = (– , 0), :@0.685042:0.689450:0.836157:0.689450:0.836157:0.674387:0.685042:0.674387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.757511:0.689556:0.764617:0.689556:0.764617:0.674520:0.757511:0.674520:0.000000
:@0.759340:0.689899:0.765197:0.689899:0.765197:0.675457:0.759340:0.675457:0.000000
1:@0.765197:0.692443:0.769719:0.692443:0.769719:0.683662:0.765197:0.683662:0.000000
a:@0.802173:0.689556:0.810370:0.689556:0.810370:0.674519:0.802173:0.674519:0.000000
v:@0.638503:0.705398:0.645609:0.705398:0.645609:0.690362:0.638503:0.690362:0.000000
:@0.640333:0.705741:0.646190:0.705741:0.646190:0.691299:0.640333:0.691299:0.000000
2:@0.646189:0.708285:0.650712:0.708285:0.650712:0.699504:0.646189:0.699504:0.000000
 = ( , 0) se llaman vértices de :@0.650713:0.705292:0.842407:0.705292:0.842407:0.690229:0.650713:0.690229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.673580:0.705398:0.681776:0.705398:0.681776:0.690361:0.673580:0.690361:0.000000
la hipérbola.:@0.638505:0.721134:0.718010:0.721134:0.718010:0.706071:0.638505:0.706071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la ecuación :@0.638505:0.744422:0.734263:0.744422:0.734263:0.729359:0.638505:0.729359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )   :@0.733684:0.744482:0.784179:0.744482:0.784179:0.729123:0.733684:0.729123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.739011:0.744590:0.758507:0.744590:0.758507:0.729257:0.739011:0.729257:0.000000:0.000000:0.000000
:@0.766877:0.743999:0.780518:0.743999:0.780518:0.731549:0.766877:0.731549:0.000000
:@0.783574:0.743470:0.795961:0.743470:0.795961:0.731495:0.783574:0.731495:0.000000
2:@0.795755:0.738568:0.800366:0.738568:0.800366:0.729614:0.795755:0.729614:0.000000
 tal que:@0.800241:0.744416:0.846644:0.744416:0.846644:0.729353:0.800241:0.729353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        –        = 1, se sigue que:@0.638501:0.767387:0.812093:0.767387:0.812093:0.752324:0.638501:0.752324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        =         – 1, y como         ≥ 0,:@0.638501:0.797487:0.843423:0.797487:0.843423:0.782423:0.638501:0.782423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resulta que         – 1 ≥ 0,:@0.638501:0.824022:0.790283:0.824022:0.790283:0.808959:0.638501:0.808959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de donde         ≥ 1, con lo que :@0.638501:0.854122:0.836035:0.854122:0.836035:0.839059:0.638501:0.839059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.669266:0.877198:0.679873:0.877198:0.679873:0.862161:0.669266:0.862161:0.000000:0.000000
:@0.679877:0.876670:0.693518:0.876670:0.693518:0.864219:0.679877:0.864219:0.000000
 ]–∞, – ]   [ , ∞[.:@0.693518:0.877086:0.815890:0.877086:0.815890:0.862023:0.693518:0.862023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.740273:0.877192:0.748469:0.877192:0.748469:0.862155:0.740273:0.862155:0.000000
<:@0.757598:0.876888:0.772250:0.876888:0.772250:0.863515:0.757598:0.863515:0.000000
a:@0.781379:0.877192:0.789576:0.877192:0.789576:0.862155:0.781379:0.862155:0.000000
x:@0.646101:0.760968:0.652925:0.760968:0.652925:0.745932:0.646101:0.745932:0.000000
a:@0.645415:0.775885:0.653611:0.775885:0.653611:0.760849:0.645415:0.760849:0.000000
y:@0.646003:0.791143:0.653022:0.791143:0.653022:0.776107:0.646003:0.776107:0.000000
b:@0.645282:0.806060:0.653743:0.806060:0.653743:0.791025:0.645282:0.791025:0.000000
y:@0.796775:0.791143:0.803793:0.791143:0.803793:0.776107:0.796775:0.776107:0.000000
b:@0.796054:0.806060:0.804514:0.806060:0.804514:0.791025:0.796054:0.791025:0.000000
y:@0.687812:0.760968:0.694830:0.760968:0.694830:0.745932:0.687812:0.745932:0.000000
b:@0.687091:0.775885:0.695552:0.775885:0.695552:0.760849:0.687091:0.760849:0.000000
x:@0.690310:0.791143:0.697135:0.791143:0.697135:0.776107:0.690310:0.776107:0.000000
a:@0.689624:0.806060:0.697821:0.806060:0.697821:0.791025:0.689624:0.791025:0.000000
x:@0.722140:0.817577:0.728964:0.817577:0.728964:0.802541:0.722140:0.802541:0.000000
a:@0.721454:0.832494:0.729650:0.832494:0.729650:0.817458:0.721454:0.817458:0.000000
x:@0.712088:0.847752:0.718913:0.847752:0.718913:0.832716:0.712088:0.832716:0.000000
a:@0.711402:0.862669:0.719599:0.862669:0.719599:0.847633:0.711402:0.847633:0.000000
2:@0.661580:0.755546:0.666102:0.755546:0.666102:0.746765:0.661580:0.746765:0.000000
2:@0.661580:0.785723:0.666102:0.785723:0.666102:0.776941:0.661580:0.776941:0.000000
2:@0.812351:0.785723:0.816874:0.785723:0.816874:0.776941:0.812351:0.776941:0.000000
2:@0.703039:0.755546:0.707561:0.755546:0.707561:0.746765:0.703039:0.746765:0.000000
2:@0.705438:0.785723:0.709960:0.785723:0.709960:0.776941:0.705438:0.776941:0.000000
2:@0.737268:0.812159:0.741790:0.812159:0.741790:0.803378:0.737268:0.803378:0.000000
2:@0.727219:0.842336:0.731741:0.842336:0.731741:0.833555:0.727219:0.833555:0.000000
Competencia :@0.684804:0.651990:0.782426:0.651990:0.782426:0.636518:0.684804:0.636518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684804:0.664558:0.768866:0.664558:0.768866:0.649086:0.684804:0.649086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000