160:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
Una parábola es el lugar geométrico de los puntos en un plano que equidistan de un :@0.287495:0.460112:0.907619:0.460112:0.907619:0.443723:0.287495:0.443723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto fijo llamado foco y de una recta fija llamada directriz.:@0.287495:0.476708:0.720796:0.476708:0.720796:0.460319:0.287495:0.460319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elementos de la parábola:@0.287495:0.516594:0.542900:0.516594:0.542900:0.495084:0.287495:0.495084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El eje focal es la recta que contiene al foco y es perpendicular a la directriz. Es el eje :@0.287495:0.539376:0.907659:0.539376:0.907659:0.522987:0.287495:0.522987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de simetría de la parábola.:@0.287495:0.555972:0.479860:0.555972:0.479860:0.539583:0.287495:0.539583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El punto en el que la curva corta al eje focal se llama vértice.:@0.287495:0.579691:0.726101:0.579691:0.726101:0.563302:0.287495:0.563302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el diagrama, las coordenadas del vértice son  (0, 0), las del foco  ( , 0) y la recta :@0.287495:0.603410:0.907549:0.603410:0.907549:0.587021:0.287495:0.587021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.644899:0.603410:0.654021:0.603410:0.654021:0.587049:0.644899:0.587049:0.000000
F p:@0.787363:0.603410:0.809569:0.603410:0.809569:0.587049:0.787363:0.587049:0.000000:0.000000:0.000000
directriz está dada por   = – .:@0.287495:0.620007:0.502913:0.620007:0.502913:0.603618:0.287495:0.603618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.454706:0.620007:0.462169:0.620007:0.462169:0.603645:0.454706:0.603645:0.000000
p:@0.490437:0.620007:0.499706:0.620007:0.499706:0.603645:0.490437:0.603645:0.000000
El segmento :@0.287495:0.643726:0.382748:0.643726:0.382748:0.627337:0.287495:0.627337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DE:@0.382508:0.643726:0.402171:0.643726:0.402171:0.627364:0.382508:0.627364:0.000000:0.000000
, perpendicular al eje focal, que une dos puntos de la parábola y pasa :@0.402171:0.643726:0.907770:0.643726:0.907770:0.627337:0.402171:0.627337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por el foco se llama lado recto y su longitud es 4 .:@0.287495:0.660322:0.652910:0.660322:0.652910:0.643933:0.287495:0.643933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.640434:0.660322:0.649704:0.660322:0.649704:0.643961:0.640434:0.643961:0.000000
Ecuación cartesiana de la parábola:@0.287495:0.693013:0.586783:0.693013:0.586783:0.674576:0.287495:0.674576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por definición, igualemos las distancias del punto  ( ,  ) al foco  ( , 0) y a la recta   = – : :@0.287495:0.716423:0.907696:0.716423:0.907696:0.700034:0.287495:0.700034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P x y:@0.640790:0.716423:0.675379:0.716423:0.675379:0.700061:0.640790:0.700061:0.000000:0.000000:0.000000:0.000000:0.000000
F p:@0.734052:0.716423:0.755889:0.716423:0.755889:0.700061:0.734052:0.700061:0.000000:0.000000:0.000000
x:@0.857204:0.716423:0.864667:0.716423:0.864667:0.700061:0.857204:0.700061:0.000000
p:@0.891369:0.716423:0.900638:0.716423:0.900638:0.700061:0.891369:0.700061:0.000000
(:@0.488822:0.745020:0.493706:0.745020:0.493706:0.728631:0.488822:0.728631:0.000000
):@0.530395:0.745020:0.535278:0.745020:0.535278:0.728631:0.530395:0.728631:0.000000
(:@0.557410:0.745020:0.562293:0.745020:0.562293:0.728631:0.557410:0.728631:0.000000
) 0:@0.597822:0.745020:0.597282:0.745020:0.597282:0.728631:0.597822:0.728631:0.000000:0.000000:0.000000
(:@0.476310:0.768283:0.481193:0.768283:0.481193:0.751894:0.476310:0.751894:0.000000
):@0.517883:0.768283:0.522766:0.768283:0.522766:0.751894:0.517883:0.751894:0.000000
(:@0.579173:0.768283:0.584056:0.768283:0.584056:0.751894:0.579173:0.751894:0.000000
):@0.621059:0.768283:0.625942:0.768283:0.625942:0.751894:0.621059:0.751894:0.000000
xp:@0.495456:0.745020:0.529805:0.745020:0.529805:0.728659:0.495456:0.728659:0.000000:0.000000
y:@0.564302:0.745020:0.571784:0.745020:0.571784:0.728659:0.564302:0.728659:0.000000
x p:@0.628965:0.745020:0.663609:0.745020:0.663609:0.728659:0.628965:0.728659:0.000000:0.000000:0.000000
xp:@0.482944:0.768283:0.517293:0.768283:0.517293:0.751921:0.482944:0.751921:0.000000:0.000000
y:@0.546869:0.768283:0.554351:0.768283:0.554351:0.751921:0.546869:0.751921:0.000000
x p:@0.585825:0.768283:0.620469:0.768283:0.620469:0.751921:0.585825:0.751921:0.000000:0.000000:0.000000
x:@0.478024:0.790881:0.485487:0.790881:0.485487:0.774520:0.478024:0.774520:0.000000
pxp:@0.518859:0.790881:0.562736:0.790881:0.562736:0.774520:0.518859:0.774520:0.000000:0.000000:0.000000
y:@0.587392:0.790881:0.594873:0.790881:0.594873:0.774520:0.587392:0.774520:0.000000
x:@0.621428:0.790881:0.628891:0.790881:0.628891:0.774520:0.621428:0.774520:0.000000
px p:@0.662577:0.790881:0.706453:0.790881:0.706453:0.774520:0.662577:0.774520:0.000000:0.000000:0.000000:0.000000
y:@0.478300:0.813480:0.485782:0.813480:0.485782:0.797119:0.478300:0.797119:0.000000
−:@0.507047:0.745712:0.517164:0.745712:0.517164:0.730139:0.507047:0.730139:0.000000
+:@0.545008:0.745712:0.555125:0.745712:0.555125:0.730139:0.545008:0.730139:0.000000
−:@0.575893:0.745712:0.586010:0.745712:0.586010:0.730139:0.575893:0.730139:0.000000
= +:@0.614536:0.745712:0.650672:0.745712:0.650672:0.730139:0.614536:0.730139:0.000000:0.000000:0.000000
−:@0.494553:0.768974:0.504670:0.768974:0.504670:0.753401:0.494553:0.753401:0.000000
+:@0.532514:0.768974:0.542631:0.768974:0.542631:0.753401:0.532514:0.753401:0.000000
=:@0.566476:0.768974:0.576593:0.768974:0.576593:0.753401:0.566476:0.753401:0.000000
+:@0.597416:0.768974:0.607533:0.768974:0.607533:0.753401:0.597416:0.753401:0.000000
−:@0.497004:0.791573:0.507121:0.791573:0.507121:0.776000:0.497004:0.776000:0.000000
+:@0.539664:0.791573:0.549781:0.791573:0.549781:0.776000:0.539664:0.776000:0.000000
+:@0.573018:0.791573:0.583135:0.791573:0.583135:0.776000:0.573018:0.776000:0.000000
=:@0.606999:0.791573:0.617116:0.791573:0.617116:0.776000:0.606999:0.776000:0.000000
+:@0.640380:0.791549:0.650496:0.791549:0.650496:0.775976:0.640380:0.775976:0.000000
+:@0.683353:0.791549:0.693470:0.791549:0.693470:0.775976:0.683353:0.775976:0.000000
=:@0.497880:0.814141:0.507997:0.814141:0.507997:0.798568:0.497880:0.798568:0.000000
2:@0.535101:0.737358:0.540313:0.737358:0.540313:0.727860:0.535101:0.727860:0.000000
2:@0.602532:0.737358:0.607744:0.737358:0.607744:0.727860:0.602532:0.727860:0.000000
2:@0.522584:0.760618:0.527796:0.760618:0.527796:0.751120:0.522584:0.751120:0.000000
2:@0.555937:0.760618:0.561149:0.760618:0.561149:0.751120:0.555937:0.751120:0.000000
2:@0.625771:0.760618:0.630983:0.760618:0.630983:0.751120:0.625771:0.751120:0.000000
2:@0.487096:0.783213:0.492308:0.783213:0.492308:0.773715:0.487096:0.773715:0.000000
2:@0.563114:0.783213:0.568325:0.783213:0.568325:0.773715:0.563114:0.773715:0.000000
2:@0.596456:0.783213:0.601667:0.783213:0.601667:0.773715:0.596456:0.773715:0.000000
2:@0.630481:0.783213:0.635692:0.783213:0.635692:0.773715:0.630481:0.773715:0.000000
2:@0.706808:0.783213:0.712020:0.783213:0.712020:0.773715:0.706808:0.773715:0.000000
2:@0.487352:0.805808:0.492564:0.805808:0.492564:0.796310:0.487352:0.796310:0.000000
2:@0.509398:0.790871:0.518390:0.790871:0.518390:0.774482:0.509398:0.774482:0.000000
2:@0.653096:0.790871:0.662089:0.790871:0.662089:0.774482:0.653096:0.774482:0.000000
4 4:@0.511492:0.813464:0.520484:0.813464:0.520484:0.797075:0.511492:0.797075:0.000000:0.000000:0.000000
px:@0.521535:0.813464:0.538212:0.813464:0.538212:0.797102:0.521535:0.797102:0.000000:0.000000
Esta es la ecuación cartesiana de la parábola con vértice en el origen y eje focal :@0.287485:0.843088:0.907741:0.843088:0.907741:0.826699:0.287485:0.826699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
horizontal. :@0.287485:0.859685:0.368549:0.859685:0.368549:0.843296:0.287485:0.843296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   < 0, o sea,   = –4 , la parábola se abre hacia la izquierda.:@0.287485:0.883404:0.738607:0.883402:0.738607:0.867013:0.287485:0.867015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.303923:0.883404:0.313192:0.883404:0.313192:0.867042:0.303923:0.867042:0.000000
y:@0.393739:0.883404:0.401221:0.883404:0.401221:0.867042:0.393739:0.867042:0.000000
2:@0.401227:0.877355:0.406470:0.877355:0.406470:0.867800:0.401227:0.867800:0.000000
px:@0.443732:0.883402:0.460298:0.883402:0.460298:0.867041:0.443732:0.867041:0.000000:0.000000
Si el eje focal es vertical, la ecuación es:   = –4 .:@0.287502:0.907121:0.645787:0.907126:0.645787:0.890737:0.287502:0.890732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.575983:0.907121:0.583446:0.907121:0.583446:0.890760:0.575983:0.890760:0.000000
2:@0.583437:0.901079:0.588679:0.901079:0.588679:0.891524:0.583437:0.891524:0.000000
py:@0.625941:0.907126:0.642581:0.907126:0.642581:0.890765:0.625941:0.890765:0.000000:0.000000
nidad de conocimientos:@0.306727:0.432755:0.480398:0.432755:0.480398:0.417391:0.306727:0.417391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.433541:0.297460:0.433541:0.297460:0.416406:0.284892:0.416406:0.000000
Pienso y progreso:@0.294883:0.370192:0.417347:0.370192:0.417347:0.354828:0.294883:0.354828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Averigua sobre la aplicación de la parábola en física.:@0.294883:0.388843:0.639679:0.388843:0.639679:0.373944:0.294883:0.373944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los puentes colgantes utilizan cables con forma parabólica, porque esta geometría :@0.287495:0.168345:0.907733:0.168345:0.907733:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distribuye eficientemente las cargas hacia las torres de soporte y equilibran las fuer-:@0.287495:0.184941:0.903642:0.184941:0.903642:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
zas de tensión, lo cual permite una estructura estable y resistente, optimizando ma-:@0.287495:0.201538:0.903723:0.201538:0.903723:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teriales y garantizando seguridad.:@0.287495:0.218134:0.533298:0.218134:0.533298:0.201745:0.287495:0.201745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un puente colgante tiene dos torres de soporte de 40 metros de altura, separadas :@0.287495:0.241853:0.907713:0.241853:0.907713:0.225464:0.287495:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por una distancia de 100 metros. El cable principal que cuelga entre ellas forma una :@0.287495:0.258450:0.907604:0.258450:0.907604:0.242061:0.287495:0.242061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
parábola, y su punto más bajo está 10 metros por encima del nivel del puente.:@0.287495:0.275046:0.860460:0.275046:0.860460:0.258657:0.287495:0.258657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.287495:0.298765:0.302403:0.298765:0.302403:0.281864:0.287495:0.281864:0.000000:0.000000
  Determina la ecuación cartesiana de la parábola que describe la forma del cable, :@0.302403:0.298765:0.907746:0.298765:0.907746:0.282376:0.302403:0.282376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
considerando que el vértice está en el punto más bajo.:@0.315985:0.315361:0.716944:0.315361:0.716944:0.298972:0.315985:0.298972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287495:0.335526:0.303712:0.335526:0.303712:0.318625:0.287495:0.318625:0.000000:0.000000
  Calcula la altura del cable a 30 metros de una de las torres.:@0.303712:0.335526:0.741766:0.335526:0.741766:0.319137:0.303712:0.319137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Escribe situaciones en :@0.097599:0.192000:0.247834:0.192000:0.247834:0.177101:0.097599:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde aprecies arcos. :@0.099777:0.207088:0.247833:0.207088:0.247833:0.192189:0.099777:0.192189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Secciones cónicas. La parábola:@0.286308:0.075160:0.736495:0.075160:0.736495:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.094760:0.108603:0.159692:0.108603:0.159692:0.011514:0.094760:0.011514:0.000000
–2:@0.149722:0.523038:0.155043:0.523038:0.155043:0.518580:0.149722:0.518580:0.000000:0.000000
–1:@0.149722:0.509146:0.155043:0.509146:0.155043:0.504687:0.149722:0.504687:0.000000:0.000000
–4:@0.149722:0.551222:0.155043:0.551222:0.155043:0.546763:0.149722:0.546763:0.000000:0.000000
–3:@0.149722:0.537329:0.155043:0.537329:0.155043:0.532870:0.149722:0.532870:0.000000:0.000000
1:@0.151991:0.481199:0.154686:0.481199:0.154686:0.476740:0.151991:0.476740:0.000000
2:@0.151991:0.467815:0.154686:0.467815:0.154686:0.463356:0.151991:0.463356:0.000000
3:@0.151991:0.453761:0.154686:0.453761:0.154686:0.449302:0.151991:0.449302:0.000000
–2:@0.116483:0.498044:0.121804:0.498044:0.121804:0.493586:0.116483:0.493586:0.000000:0.000000
–3:@0.097925:0.498044:0.103246:0.498044:0.103246:0.493586:0.097925:0.493586:0.000000:0.000000
–4:@0.079478:0.498044:0.084798:0.498044:0.084798:0.493586:0.079478:0.493586:0.000000:0.000000
–1:@0.135198:0.498044:0.140519:0.498044:0.140519:0.493586:0.135198:0.493586:0.000000:0.000000
1:@0.173585:0.498044:0.176280:0.498044:0.176280:0.493586:0.173585:0.493586:0.000000
2:@0.192479:0.498044:0.195174:0.498044:0.195174:0.493586:0.192479:0.493586:0.000000
3:@0.211011:0.498044:0.213705:0.498044:0.213705:0.493586:0.211011:0.493586:0.000000
4:@0.229527:0.498044:0.232221:0.498044:0.232221:0.493586:0.229527:0.493586:0.000000
5:@0.248174:0.498044:0.250868:0.498044:0.250868:0.493586:0.248174:0.493586:0.000000
0:@0.152091:0.498044:0.154786:0.498044:0.154786:0.493586:0.152091:0.493586:0.000000
y:@0.151875:0.440287:0.153902:0.440287:0.153902:0.436413:0.151875:0.436413:0.000000
x:@0.256572:0.497420:0.258599:0.497420:0.258599:0.493546:0.256572:0.493546:0.000000
P x  y:@0.197192:0.455304:0.206669:0.455304:0.206669:0.451430:0.197192:0.451430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ):@0.199522:0.455304:0.207974:0.455304:0.207974:0.451402:0.199522:0.451402:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.123216:0.443724:0.125243:0.443724:0.125243:0.439850:0.123216:0.439850:0.000000
 = :@0.125243:0.443724:0.132229:0.443724:0.132229:0.439822:0.125243:0.439822:0.000000:0.000000:0.000000:0.000000
p:@0.132229:0.443724:0.134642:0.443724:0.134642:0.439850:0.132229:0.439850:0.000000
F p  0:@0.179220:0.492666:0.189125:0.492666:0.189125:0.488792:0.179220:0.488792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ):@0.181358:0.492666:0.190431:0.492666:0.190431:0.488764:0.181358:0.488764:0.000000:0.000000:0.000000:0.000000:0.000000
V 0  0:@0.154383:0.492010:0.164476:0.492010:0.164476:0.488136:0.154383:0.488136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ):@0.156860:0.492010:0.165781:0.492010:0.165781:0.488109:0.156860:0.488109:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.171228:0.465135:0.173388:0.465135:0.173388:0.461261:0.171228:0.461261:0.000000
D:@0.176352:0.520852:0.179326:0.520852:0.179326:0.516978:0.176352:0.516978:0.000000
Geométricamente, la :@0.104927:0.623601:0.248426:0.623601:0.248426:0.608702:0.104927:0.608702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
parábola también se :@0.107976:0.638689:0.248428:0.638689:0.248428:0.623790:0.107976:0.623790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puede definir como la :@0.097522:0.653776:0.248428:0.653776:0.248428:0.638877:0.097522:0.638877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
curva que resulta al cortar :@0.071992:0.668864:0.248425:0.668864:0.248425:0.653965:0.071992:0.653965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un cono circular recto con :@0.069847:0.683952:0.248426:0.683952:0.248426:0.669053:0.069847:0.669053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un plano paralelo a una :@0.087287:0.699039:0.248428:0.699039:0.248428:0.684140:0.087287:0.684140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las generatrices del :@0.095847:0.714127:0.248426:0.714127:0.248426:0.699228:0.095847:0.699228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cono; es decir, cuando el :@0.080552:0.729214:0.248426:0.729214:0.248426:0.714315:0.080552:0.714315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
plano secante es paralelo :@0.075912:0.744302:0.248426:0.744302:0.248426:0.729403:0.075912:0.729403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a una de las líneas que :@0.094574:0.759390:0.248428:0.759390:0.248428:0.744491:0.094574:0.744491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma la superficie del :@0.097388:0.774477:0.248426:0.774477:0.248426:0.759578:0.097388:0.759578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cono.:@0.207870:0.789565:0.244759:0.789565:0.244759:0.774666:0.207870:0.774666:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.130759:0.805067:0.139755:0.805067:0.139755:0.790194:0.130759:0.790194:0.000000
O:@0.126071:0.900945:0.136876:0.900945:0.136876:0.886072:0.126071:0.886072:0.000000
plano:@0.159794:0.835013:0.198090:0.835013:0.198090:0.820114:0.159794:0.820114:0.000000:0.000000:0.000000:0.000000:0.000000
eje:@0.145973:0.864886:0.165808:0.864886:0.165808:0.849987:0.145973:0.849987:0.000000:0.000000:0.000000
     Matemática:@0.115799:0.591160:0.223340:0.591160:0.223340:0.574260:0.115799:0.574260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.070380:0.318022:0.070380:0.275196:0.058469:0.275196:0.058469:0.318022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100 m:@0.136439:0.265893:0.178354:0.265893:0.178354:0.251648:0.136439:0.251648:0.000000:0.000000:0.000000:0.000000:0.000000
40m:@0.257442:0.301375:0.257442:0.278806:0.238461:0.278806:0.238461:0.301375:0.000000:0.000000:0.000000
Las parábolas son esenciales :@0.072616:0.368896:0.246425:0.368896:0.246425:0.355487:0.072616:0.355487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la ingeniería de puentes, :@0.072616:0.381468:0.241597:0.381468:0.241597:0.368059:0.072616:0.368059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ya que su forma distribuye :@0.072616:0.394039:0.234722:0.394039:0.234722:0.380630:0.072616:0.380630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eficientemente las cargas. :@0.072616:0.406611:0.230380:0.406611:0.230380:0.393202:0.072616:0.393202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000