132:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Funciones racionales y cónicas:@0.073089:0.043661:0.343993:0.043661:0.343993:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Verifica el siguiente ejemplo resuelto.:@0.073089:0.136836:0.385333:0.136836:0.385333:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La ecuación cartesiana de una hipérbola es::@0.104632:0.167776:0.442148:0.167774:0.442148:0.152061:0.104632:0.152063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) tal que 1.:@0.104633:0.198710:0.318513:0.198710:0.318513:0.182997:0.104633:0.182997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.109437:0.198710:0.131360:0.198710:0.131360:0.183275:0.109437:0.183275:0.000000:0.000000:0.000000 [:@0.140047:0.198420:0.154683:0.198420:0.154683:0.185010:0.140047:0.185010:0.000000 R:@0.158553:0.197850:0.171843:0.197850:0.171843:0.184953:0.158553:0.184953:0.000000 2:@0.171744:0.192646:0.176981:0.192646:0.176981:0.183485:0.171744:0.183485:0.000000 x:@0.234934:0.198710:0.242389:0.198710:0.242389:0.183275:0.234934:0.183275:0.000000 2:@0.242316:0.192646:0.247552:0.192646:0.247552:0.183485:0.242316:0.183485:0.000000 2:@0.251464:0.198155:0.266797:0.198155:0.266797:0.184439:0.251464:0.184439:0.000000 y:@0.270663:0.198710:0.278136:0.198710:0.278136:0.183275:0.270663:0.183275:0.000000 2:@0.278056:0.192646:0.283293:0.192646:0.283293:0.183485:0.278056:0.183485:0.000000 5:@0.287203:0.198155:0.302536:0.198155:0.302536:0.184439:0.287203:0.184439:0.000000 Obtén:@0.104639:0.229650:0.152918:0.229650:0.152918:0.212980:0.104639:0.212980:0.000000:0.000000:0.000000:0.000000:0.000000 los focos, las asíntotas, la excentricidad, y :@0.152830:0.229650:0.454272:0.229650:0.454272:0.213937:0.152830:0.213937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 traza:@0.453917:0.229650:0.491260:0.229650:0.491260:0.212980:0.453917:0.212980:0.000000:0.000000:0.000000:0.000000:0.000000 la hipérbola.:@0.491173:0.229650:0.584327:0.229650:0.584327:0.213937:0.491173:0.213937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En primer lugar, se tiene 1, luego, la hipérbola es equilátera. Sus focos son ( 2 , 0), pues 2; 2 .:@0.104639:0.260590:0.897065:0.260583:0.897065:0.244871:0.104639:0.244877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.271078:0.260590:0.280337:0.260590:0.280337:0.245154:0.271078:0.245154:0.000000 5 5:@0.283300:0.260035:0.329134:0.260035:0.329134:0.246319:0.283300:0.246319:0.000000:0.000000:0.000000 b:@0.301579:0.260590:0.310837:0.260590:0.310837:0.245154:0.301579:0.245154:0.000000 2:@0.671441:0.263756:0.676677:0.263756:0.676677:0.254595:0.671441:0.254595:0.000000 5:@0.679859:0.260029:0.695193:0.260029:0.695193:0.246313:0.679859:0.246313:0.000000 c:@0.787008:0.260583:0.794665:0.260583:0.794665:0.245148:0.787008:0.245148:0.000000 5:@0.797629:0.260029:0.812962:0.260029:0.812962:0.246313:0.797629:0.246313:0.000000 a:@0.844439:0.260583:0.853697:0.260583:0.853697:0.245148:0.844439:0.245148:0.000000 5:@0.856661:0.260029:0.871994:0.260029:0.871994:0.246313:0.856661:0.246313:0.000000 Por otro lado, de esta ecuación se obtiene:@0.104614:0.291523:0.407981:0.291523:0.407981:0.275811:0.104614:0.275811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.104614:0.322463:0.112069:0.322463:0.112069:0.307028:0.104614:0.307028:0.000000 2:@0.112021:0.316394:0.117258:0.316394:0.117258:0.307234:0.112021:0.307234:0.000000 1. Como 0, :@0.117211:0.322458:0.292561:0.322458:0.292561:0.306746:0.117211:0.306746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.121169:0.321904:0.136502:0.321904:0.136502:0.308188:0.121169:0.308188:0.000000 y:@0.140368:0.322458:0.147841:0.322458:0.147841:0.307023:0.140368:0.307023:0.000000 2:@0.147761:0.316394:0.152998:0.316394:0.152998:0.307234:0.147761:0.307234:0.000000 5:@0.156908:0.321904:0.172241:0.321904:0.172241:0.308188:0.156908:0.308188:0.000000 y:@0.240753:0.322458:0.248226:0.322458:0.248226:0.307023:0.240753:0.307023:0.000000 2:@0.248146:0.316394:0.253383:0.316394:0.253383:0.307234:0.248146:0.307234:0.000000 $:@0.257292:0.321904:0.272626:0.321904:0.272626:0.308188:0.257292:0.308188:0.000000 ;:@0.292450:0.321904:0.304728:0.321904:0.304728:0.308188:0.292450:0.308188:0.000000 y:@0.304636:0.322458:0.312109:0.322458:0.312109:0.307023:0.304636:0.307023:0.000000 , se sigue que :@0.312036:0.322458:0.449971:0.322458:0.449971:0.306746:0.312036:0.306746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.315996:0.322168:0.330633:0.322168:0.330633:0.308758:0.315996:0.308758:0.000000 R:@0.334502:0.321598:0.347793:0.321598:0.347793:0.308701:0.334502:0.308701:0.000000 x:@0.104633:0.353398:0.112088:0.353398:0.112088:0.337963:0.104633:0.337963:0.000000 2:@0.112021:0.347331:0.117258:0.347331:0.117258:0.338170:0.112021:0.338170:0.000000 1 0, con lo que 1 equivale a | | 1, es decir, :@0.117211:0.353394:0.512115:0.353394:0.512115:0.337682:0.117211:0.337682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 $:@0.121169:0.352840:0.168549:0.352840:0.168549:0.339124:0.121169:0.339124:0.000000:0.000000:0.000000 x:@0.269826:0.353394:0.277281:0.353394:0.277281:0.337959:0.269826:0.337959:0.000000 2:@0.277211:0.347331:0.282448:0.347331:0.282448:0.338170:0.277211:0.338170:0.000000 $:@0.286357:0.352840:0.301691:0.352840:0.301691:0.339124:0.286357:0.339124:0.000000 x:@0.399783:0.353394:0.407238:0.353394:0.407238:0.337959:0.399783:0.337959:0.000000 $:@0.414932:0.352840:0.430265:0.352840:0.430265:0.339124:0.414932:0.339124:0.000000 x :@0.511957:0.353394:0.522651:0.353394:0.522651:0.337959:0.511957:0.337959:0.000000:0.000000 [:@0.522598:0.353104:0.537234:0.353104:0.537234:0.339695:0.522598:0.339695:0.000000 ]:@0.537146:0.353394:0.545982:0.353394:0.545982:0.337682:0.537146:0.337682:0.000000:0.000000 2` 2:@0.545890:0.352840:0.595718:0.352840:0.595718:0.339124:0.545890:0.339124:0.000000:0.000000:0.000000:0.000000 , 1] [1, [.:@0.573317:0.353394:0.672747:0.353394:0.672747:0.337682:0.573317:0.337682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.613285:0.353104:0.627922:0.353104:0.627922:0.339695:0.613285:0.339695:0.000000 `:@0.652555:0.352840:0.664832:0.352840:0.664832:0.339124:0.652555:0.339124:0.000000 Para :@0.104626:0.384334:0.139187:0.384334:0.139187:0.368622:0.104626:0.368622:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.139489:0.384334:0.150184:0.384334:0.150184:0.368899:0.139489:0.368899:0.000000:0.000000 [:@0.150460:0.384042:0.165096:0.384042:0.165096:0.370632:0.150460:0.370632:0.000000 ]:@0.165008:0.384332:0.174231:0.384332:0.174231:0.368619:0.165008:0.368619:0.000000:0.000000 2` 2:@0.174157:0.383777:0.224390:0.383777:0.224390:0.370061:0.174157:0.370061:0.000000:0.000000:0.000000:0.000000 , 1] de la ecuación 1 se obtiene la rama de hipérbola que se muestra a la izquierda de la :@0.201584:0.384332:0.931172:0.384332:0.931172:0.368619:0.201584:0.368619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.352615:0.384332:0.360089:0.384332:0.360089:0.368897:0.352615:0.368897:0.000000 2:@0.360032:0.378268:0.365269:0.378268:0.365269:0.369107:0.360032:0.369107:0.000000 5:@0.369567:0.383777:0.384900:0.383777:0.384900:0.370061:0.369567:0.370061:0.000000 x:@0.389152:0.384332:0.396607:0.384332:0.396607:0.368897:0.389152:0.368897:0.000000 2:@0.396555:0.378268:0.401792:0.378268:0.401792:0.369107:0.396555:0.369107:0.000000 2:@0.406090:0.383777:0.421423:0.383777:0.421423:0.370061:0.406090:0.370061:0.000000 figura, y para :@0.104634:0.400974:0.202202:0.400974:0.202202:0.385261:0.104634:0.385261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.202358:0.400974:0.213053:0.400974:0.213053:0.385538:0.202358:0.385538:0.000000:0.000000 [:@0.213266:0.400684:0.227902:0.400684:0.227902:0.387274:0.213266:0.387274:0.000000 [1, [ de la ecuación 1 se obtiene la rama de la hipérbola que se muestra a la derecha :@0.227814:0.400974:0.931345:0.400974:0.931345:0.385261:0.227814:0.385261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 `:@0.253198:0.400419:0.265475:0.400419:0.265475:0.386703:0.253198:0.386703:0.000000 y:@0.384515:0.400974:0.391988:0.400974:0.391988:0.385538:0.384515:0.385538:0.000000 2:@0.391928:0.394910:0.397165:0.394910:0.397165:0.385749:0.391928:0.385749:0.000000 5:@0.401406:0.400419:0.416739:0.400419:0.416739:0.386703:0.401406:0.386703:0.000000 x:@0.420936:0.400974:0.428391:0.400974:0.428391:0.385538:0.420936:0.385538:0.000000 2:@0.428309:0.394910:0.433546:0.394910:0.433546:0.385749:0.428309:0.385749:0.000000 2:@0.437787:0.400419:0.453120:0.400419:0.453120:0.386703:0.437787:0.386703:0.000000 de la Figura 2,40.:@0.104634:0.417615:0.225397:0.417615:0.225397:0.401903:0.104634:0.401903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.376354:0.484256:0.381789:0.484256:0.381789:0.473030:0.376354:0.473030:0.000000 2:@0.381789:0.479846:0.385598:0.479846:0.385598:0.473184:0.381789:0.473184:0.000000 = :@0.385598:0.484256:0.399440:0.484256:0.399440:0.472829:0.385598:0.472829:0.000000:0.000000:0.000000 x –:@0.399440:0.484256:0.415364:0.484256:0.415364:0.473030:0.399440:0.473030:0.000000:0.000000:0.000000 2:@0.404862:0.479846:0.408670:0.479846:0.408670:0.473184:0.404862:0.473184:0.000000 1:@0.415364:0.484256:0.421897:0.484256:0.421897:0.472829:0.415364:0.472829:0.000000 y:@0.602890:0.484256:0.608325:0.484256:0.608325:0.473030:0.602890:0.473030:0.000000 2:@0.608322:0.479846:0.612131:0.479846:0.612131:0.473184:0.608322:0.473184:0.000000 = :@0.612131:0.484256:0.625973:0.484256:0.625973:0.472829:0.612131:0.472829:0.000000:0.000000:0.000000 x –:@0.625973:0.484256:0.641895:0.484256:0.641895:0.473030:0.625973:0.473030:0.000000:0.000000:0.000000 2:@0.631393:0.479846:0.635202:0.479846:0.635202:0.473184:0.631393:0.473184:0.000000 1:@0.641895:0.484256:0.648428:0.484256:0.648428:0.472829:0.641895:0.472829:0.000000 0:@0.506475:0.522841:0.511374:0.522841:0.511374:0.514270:0.506475:0.514270:0.000000 y:@0.497524:0.450808:0.503978:0.450808:0.503978:0.437478:0.497524:0.437478:0.000000 x:@0.646115:0.528767:0.652553:0.528767:0.652553:0.515437:0.646115:0.515437:0.000000 –1:@0.499753:0.544349:0.509673:0.544349:0.509673:0.535779:0.499753:0.535779:0.000000:0.000000 1:@0.504773:0.490838:0.509673:0.490838:0.509673:0.482268:0.504773:0.482268:0.000000 1:@0.544733:0.522511:0.549633:0.522511:0.549633:0.513940:0.544733:0.513940:0.000000 2:@0.591300:0.522511:0.596200:0.522511:0.596200:0.513940:0.591300:0.513940:0.000000 –1:@0.468869:0.522511:0.478789:0.522511:0.478789:0.513940:0.468869:0.513940:0.000000:0.000000 –2:@0.423687:0.522511:0.433607:0.522511:0.433607:0.513940:0.423687:0.513940:0.000000:0.000000 1:@0.448925:0.535642:0.453032:0.535642:0.453032:0.528459:0.448925:0.528459:0.000000 2:@0.582011:0.535642:0.586118:0.535642:0.586118:0.528459:0.582011:0.528459:0.000000 x:@0.382269:0.493715:0.387691:0.493715:0.387691:0.482490:0.382269:0.482490:0.000000 ≤ –1:@0.387691:0.493715:0.414760:0.493715:0.414760:0.482288:0.387691:0.482288:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.611443:0.493715:0.616865:0.493715:0.616865:0.482490:0.611443:0.482490:0.000000 ≥ 1:@0.616865:0.493715:0.637240:0.493715:0.637240:0.482288:0.616865:0.482288:0.000000:0.000000:0.000000:0.000000 Las rectas asíntotas de esta hipérbola están definidas como::@0.104633:0.622524:0.536382:0.622524:0.536382:0.606812:0.104633:0.606812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.104633:0.653462:0.113579:0.653462:0.113579:0.638026:0.104633:0.638026:0.000000 1:@0.113513:0.656634:0.118749:0.656634:0.118749:0.647474:0.113513:0.647474:0.000000 {( , ) | },:@0.118702:0.653462:0.276613:0.653462:0.276613:0.637749:0.118702:0.637749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.122660:0.652907:0.137993:0.652907:0.137993:0.639191:0.122660:0.639191:0.000000 x y:@0.151449:0.653462:0.173372:0.653462:0.173372:0.638026:0.151449:0.638026:0.000000:0.000000:0.000000 [:@0.182055:0.653172:0.196692:0.653172:0.196692:0.639762:0.182055:0.639762:0.000000 R:@0.200561:0.652602:0.213851:0.652602:0.213851:0.639705:0.200561:0.639705:0.000000 2:@0.213753:0.647398:0.218989:0.647398:0.218989:0.638237:0.213753:0.638237:0.000000 y:@0.230669:0.653462:0.238142:0.653462:0.238142:0.638026:0.230669:0.638026:0.000000 5:@0.242026:0.652907:0.257359:0.652907:0.257359:0.639191:0.242026:0.639191:0.000000 x:@0.261225:0.653462:0.268680:0.653462:0.268680:0.638026:0.261225:0.638026:0.000000 R:@0.104634:0.684402:0.113580:0.684402:0.113580:0.668966:0.104634:0.668966:0.000000 2:@0.113513:0.687570:0.118749:0.687570:0.118749:0.678410:0.113513:0.678410:0.000000 {( , ) | :@0.118703:0.684398:0.261298:0.684398:0.261298:0.668685:0.118703:0.668685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.122660:0.683843:0.137993:0.683843:0.137993:0.670128:0.122660:0.670128:0.000000 x y:@0.151449:0.684398:0.173372:0.684398:0.173372:0.668963:0.151449:0.668963:0.000000:0.000000:0.000000 [:@0.182055:0.684108:0.196692:0.684108:0.196692:0.670698:0.182055:0.670698:0.000000 R:@0.200561:0.683538:0.213851:0.683538:0.213851:0.670641:0.200561:0.670641:0.000000 2:@0.213753:0.678334:0.218989:0.678334:0.218989:0.669174:0.213753:0.669174:0.000000 y:@0.230669:0.684398:0.238142:0.684398:0.238142:0.668963:0.230669:0.668963:0.000000 5 2:@0.242026:0.683843:0.276558:0.683843:0.276558:0.670128:0.242026:0.670128:0.000000:0.000000:0.000000 x:@0.276466:0.684398:0.283921:0.684398:0.283921:0.668963:0.276466:0.668963:0.000000 }.:@0.283847:0.684398:0.291855:0.684398:0.291855:0.668685:0.283847:0.668685:0.000000:0.000000 En la figura de arriba, se muestran con línea punteada estas dos rectas.:@0.104634:0.715338:0.614103:0.715338:0.614103:0.699625:0.104634:0.699625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La excentricidad de esta hipérbola es::@0.104634:0.746278:0.376174:0.746278:0.376174:0.730565:0.104634:0.730565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.104634:0.782848:0.112421:0.782848:0.112421:0.767413:0.104634:0.767413:0.000000 :@0.112347:0.782848:0.173489:0.782841:0.173489:0.767128:0.112347:0.767136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.116305:0.782294:0.131638:0.782294:0.131638:0.768578:0.116305:0.768578:0.000000 c:@0.138797:0.775090:0.146454:0.775090:0.146454:0.759654:0.138797:0.759654:0.000000 a:@0.137839:0.789790:0.147098:0.789790:0.147098:0.774355:0.137839:0.774355:0.000000 5:@0.154217:0.782286:0.169550:0.782286:0.169550:0.768570:0.154217:0.768570:0.000000 a:@0.182151:0.790792:0.191410:0.790792:0.191410:0.775357:0.182151:0.775357:0.000000 2:@0.183218:0.776425:0.192201:0.776425:0.192201:0.760712:0.183218:0.760712:0.000000 a:@0.192183:0.776425:0.201441:0.776425:0.201441:0.760989:0.192183:0.760989:0.000000 2 .:@0.203311:0.782841:0.251519:0.782841:0.251519:0.767128:0.203311:0.767128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.207268:0.782286:0.222601:0.782286:0.222601:0.768570:0.207268:0.768570:0.000000 La rama izquierda de la hipérbola está definida como el conjunto:@0.104629:0.813781:0.575183:0.813781:0.575183:0.798068:0.104629:0.798068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , 1, 1) {( , ) | 1, 1},:@0.119498:0.844714:0.430543:0.844714:0.430543:0.829002:0.119498:0.829002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.172402:0.844160:0.187735:0.844160:0.187735:0.830444:0.172402:0.830444:0.000000 x y:@0.201190:0.844714:0.223113:0.844714:0.223113:0.829279:0.201190:0.829279:0.000000:0.000000:0.000000 [:@0.231805:0.844424:0.246441:0.844424:0.246441:0.831014:0.231805:0.831014:0.000000 R:@0.250311:0.843854:0.263601:0.843854:0.263601:0.830957:0.250311:0.830957:0.000000 2:@0.263502:0.838650:0.268739:0.838650:0.268739:0.829490:0.263502:0.829490:0.000000 x:@0.280417:0.844714:0.287872:0.844714:0.287872:0.829279:0.280417:0.829279:0.000000 2:@0.287803:0.838650:0.293040:0.838650:0.293040:0.829490:0.287803:0.829490:0.000000 2:@0.296950:0.844160:0.312283:0.844160:0.312283:0.830444:0.296950:0.830444:0.000000 y:@0.316149:0.844714:0.323622:0.844714:0.323622:0.829279:0.316149:0.829279:0.000000 2:@0.323542:0.838650:0.328779:0.838650:0.328779:0.829490:0.323542:0.829490:0.000000 5:@0.332690:0.844160:0.348023:0.844160:0.348023:0.830444:0.332690:0.830444:0.000000 x:@0.367848:0.844714:0.375303:0.844714:0.375303:0.829279:0.367848:0.829279:0.000000 # 2:@0.379187:0.844160:0.413719:0.844160:0.413719:0.830444:0.379187:0.830444:0.000000:0.000000:0.000000 y la rama derecha de la hipérbola está definida como:@0.104643:0.875654:0.488456:0.875654:0.488456:0.859942:0.104643:0.859942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ) {( , ) | 1, 1}.:@0.119498:0.907502:0.427749:0.907502:0.427749:0.891076:0.119498:0.891076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.139309:0.907502:0.165981:0.907502:0.165981:0.891366:0.139309:0.891366:0.000000:0.000000:0.000000 5:@0.175045:0.906922:0.191075:0.906922:0.191075:0.892583:0.175045:0.892583:0.000000 x y:@0.205142:0.907502:0.228062:0.907502:0.228062:0.891366:0.205142:0.891366:0.000000:0.000000:0.000000 [:@0.237172:0.907055:0.251808:0.907055:0.251808:0.893645:0.237172:0.893645:0.000000 R:@0.255852:0.906485:0.269142:0.906485:0.269142:0.893588:0.255852:0.893588:0.000000 2:@0.269048:0.901163:0.274523:0.901163:0.274523:0.891586:0.269048:0.891586:0.000000 x:@0.286733:0.907502:0.294527:0.907502:0.294527:0.891366:0.286733:0.891366:0.000000 2:@0.294455:0.901163:0.299930:0.901163:0.299930:0.891586:0.294455:0.891586:0.000000 2:@0.304018:0.906922:0.320048:0.906922:0.320048:0.892583:0.304018:0.892583:0.000000 y:@0.324089:0.907502:0.331902:0.907502:0.331902:0.891366:0.324089:0.891366:0.000000 2:@0.331818:0.901163:0.337293:0.901163:0.337293:0.891586:0.331818:0.891586:0.000000 5:@0.341383:0.906922:0.357413:0.906922:0.357413:0.892583:0.341383:0.892583:0.000000 x:@0.378139:0.907502:0.385932:0.907502:0.385932:0.891366:0.378139:0.891366:0.000000 $:@0.389993:0.906922:0.406023:0.906922:0.406023:0.892583:0.389993:0.892583:0.000000 Evaluación formativa:@0.131433:0.098522:0.446328:0.098522:0.446328:0.067281:0.131433:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.40:@0.427899:0.583796:0.485758:0.583796:0.485758:0.572368:0.427899:0.572368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000