135:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico y variacional:@0.538113:0.043660:0.926913:0.043660:0.926913:0.024915:0.538113:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Trabajo colaborativo:@0.085965:0.139452:0.241425:0.139452:0.241425:0.122783:0.085965:0.122783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Objetivo: :@0.085422:0.164641:0.160816:0.164641:0.160816:0.147971:0.085422:0.147971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entender la ecuación cartesiana de la hipérbola, cómo identificar sus características principales, en :@0.162291:0.164641:0.918207:0.164641:0.918207:0.148928:0.162291:0.148928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
particular sus asíntotas, y explorar aplicaciones prácticas.:@0.085422:0.181283:0.493259:0.181283:0.493259:0.165570:0.085422:0.165570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Introducción a la ecuación de la hipérbola:@0.085422:0.205066:0.402463:0.205066:0.402463:0.188397:0.085422:0.188397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dividan un grupo en cuatro estudiantes. Cada estudiante investigará y presentará una parte de la teoría sobre la :@0.085422:0.228850:0.919265:0.228850:0.919265:0.213138:0.085422:0.213138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación de la hipérbola::@0.085422:0.245492:0.267722:0.245492:0.267722:0.229780:0.085422:0.229780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.271935:0.093926:0.271935:0.093926:0.256222:0.085422:0.256222:0.000000:0.000000
Forma estándar de la ecuación: :@0.115623:0.271935:0.345112:0.271935:0.345112:0.256222:0.115623:0.256222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.347225:0.266036:0.351660:0.266036:0.351660:0.251752:0.347225:0.251752:0.000000
x h:@0.351593:0.266036:0.380793:0.266036:0.380793:0.252004:0.351593:0.252004:0.000000:0.000000:0.000000
2:@0.358303:0.265532:0.372242:0.265532:0.372242:0.253063:0.358303:0.253063:0.000000
):@0.380726:0.266036:0.385161:0.266036:0.385161:0.251752:0.380726:0.251752:0.000000
2:@0.385094:0.260524:0.389855:0.260524:0.389855:0.252196:0.385094:0.252196:0.000000
a:@0.361981:0.280327:0.370398:0.280327:0.370398:0.266295:0.361981:0.266295:0.000000
2:@0.370338:0.274814:0.375099:0.274814:0.375099:0.266486:0.370338:0.266486:0.000000
   :@0.392166:0.271935:0.415396:0.271935:0.415396:0.256222:0.392166:0.256222:0.000000:0.000000:0.000000
2:@0.396123:0.271380:0.411457:0.271380:0.411457:0.257665:0.396123:0.257665:0.000000
(:@0.418568:0.266036:0.423003:0.266036:0.423003:0.251752:0.418568:0.251752:0.000000
y k:@0.422936:0.266036:0.450396:0.266036:0.450396:0.252004:0.422936:0.252004:0.000000:0.000000:0.000000
2:@0.429663:0.265532:0.443602:0.265532:0.443602:0.253063:0.429663:0.253063:0.000000
):@0.450329:0.266036:0.454764:0.266036:0.454764:0.251752:0.450329:0.251752:0.000000
2:@0.454698:0.260524:0.459459:0.260524:0.459459:0.252196:0.454698:0.252196:0.000000
b:@0.432454:0.280327:0.440871:0.280327:0.440871:0.266295:0.432454:0.266295:0.000000
2:@0.440811:0.274814:0.445572:0.274814:0.445572:0.266486:0.440811:0.266486:0.000000
 =1 (horizontal) y :@0.462639:0.271935:0.589174:0.271935:0.589174:0.256222:0.462639:0.256222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.591372:0.266036:0.595807:0.266036:0.595807:0.251752:0.591372:0.251752:0.000000
x h:@0.595740:0.266036:0.624940:0.266036:0.624940:0.252004:0.595740:0.252004:0.000000:0.000000:0.000000
2:@0.602450:0.265532:0.616389:0.265532:0.616389:0.253063:0.602450:0.253063:0.000000
):@0.624874:0.266036:0.629308:0.266036:0.629308:0.251752:0.624874:0.251752:0.000000
2:@0.629243:0.260524:0.634004:0.260524:0.634004:0.252196:0.629243:0.252196:0.000000
a:@0.606128:0.280327:0.614545:0.280327:0.614545:0.266295:0.606128:0.266295:0.000000
2:@0.614485:0.274814:0.619246:0.274814:0.619246:0.266486:0.614485:0.266486:0.000000
   :@0.636313:0.271935:0.659543:0.271935:0.659543:0.256222:0.636313:0.256222:0.000000:0.000000:0.000000
2:@0.640270:0.271380:0.655604:0.271380:0.655604:0.257665:0.640270:0.257665:0.000000
(:@0.662716:0.266036:0.667150:0.266036:0.667150:0.251752:0.662716:0.251752:0.000000
y k:@0.667083:0.266036:0.694543:0.266036:0.694543:0.252004:0.667083:0.252004:0.000000:0.000000:0.000000
2:@0.673810:0.265532:0.687749:0.265532:0.687749:0.253063:0.673810:0.253063:0.000000
):@0.694476:0.266036:0.698911:0.266036:0.698911:0.251752:0.694476:0.251752:0.000000
2:@0.698846:0.260524:0.703606:0.260524:0.703606:0.252196:0.698846:0.252196:0.000000
b:@0.676601:0.280327:0.685018:0.280327:0.685018:0.266295:0.676601:0.266295:0.000000
2:@0.684958:0.274814:0.689719:0.274814:0.689719:0.266486:0.684958:0.266486:0.000000
 =1 (vertical).:@0.706786:0.271935:0.799746:0.271935:0.799746:0.256222:0.706786:0.256222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.295724:0.093926:0.295724:0.093926:0.280011:0.085422:0.280011:0.000000:0.000000
Elementos clave: centro (h, k), ejes, distancia focal, asíntotas.:@0.115623:0.295724:0.545551:0.295724:0.545551:0.280011:0.115623:0.280011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada estudiante tendrá que identificar estos elementos en ejemplos gráficos para que los semas compañeros :@0.085417:0.319508:0.918331:0.319508:0.918331:0.303795:0.085417:0.303795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visualicen cómo la ecuación representa la forma de la hipérbola.:@0.085417:0.336150:0.549815:0.336150:0.549815:0.320437:0.085417:0.320437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Exploración de las asíntotas:@0.085417:0.359934:0.294363:0.359934:0.294363:0.343264:0.085417:0.343264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.383734:0.093926:0.383734:0.093926:0.368022:0.085422:0.368022:0.000000:0.000000
Cada estudiante debe explicar la importancia de las asíntotas en la hipérbola, que son líneas hacia las cuales se :@0.115623:0.383734:0.919231:0.383734:0.919231:0.368022:0.115623:0.368022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
acercan las ramas de la curva sin tocarlas.:@0.115550:0.400376:0.413066:0.400376:0.413066:0.384663:0.115550:0.384663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.424166:0.093926:0.424166:0.093926:0.408454:0.085422:0.408454:0.000000:0.000000
Derivar las ecuaciones de las asíntotas::@0.115623:0.424166:0.393737:0.424166:0.393737:0.408454:0.115623:0.408454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para una hipérbola horizontal:   =   ±   (     ):@0.085417:0.450599:0.430014:0.450598:0.430014:0.434885:0.085417:0.434886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.305605:0.450599:0.313078:0.450599:0.313078:0.435164:0.305605:0.435164:0.000000
k:@0.331798:0.450599:0.339363:0.450599:0.339363:0.435164:0.331798:0.435164:0.000000
a:@0.363099:0.444699:0.371516:0.444699:0.371516:0.430667:0.363099:0.430667:0.000000
b:@0.363099:0.458983:0.371516:0.458983:0.371516:0.444951:0.363099:0.444951:0.000000
x:@0.385174:0.450598:0.392629:0.450598:0.392629:0.435163:0.385174:0.435163:0.000000
2:@0.396513:0.450043:0.411846:0.450043:0.411846:0.436327:0.396513:0.436327:0.000000
h:@0.415712:0.450598:0.425210:0.450598:0.425210:0.435163:0.415712:0.435163:0.000000
Para una hipérbola vertical:   =   ±   (     ):@0.085412:0.477031:0.409266:0.477029:0.409266:0.461317:0.085412:0.461318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.284855:0.477031:0.292328:0.477031:0.292328:0.461595:0.284855:0.461595:0.000000
k:@0.311048:0.477031:0.318614:0.477031:0.318614:0.461595:0.311048:0.461595:0.000000
a:@0.342349:0.471132:0.350766:0.471132:0.350766:0.457099:0.342349:0.457099:0.000000
b:@0.342349:0.485416:0.350766:0.485416:0.350766:0.471384:0.342349:0.471384:0.000000
x:@0.364426:0.477029:0.371881:0.477029:0.371881:0.461594:0.364426:0.461594:0.000000
2:@0.375765:0.476475:0.391098:0.476475:0.391098:0.462759:0.375765:0.462759:0.000000
h:@0.394964:0.477029:0.404462:0.477029:0.404462:0.461594:0.394964:0.461594:0.000000
• :@0.085422:0.500818:0.093926:0.500818:0.093926:0.485106:0.085422:0.485106:0.000000:0.000000
En grupo para graficar la hipérbola y sus asíntotas en papel milimetrado o mediante herramientas digitales :@0.115623:0.500818:0.918244:0.500818:0.918244:0.485106:0.115623:0.485106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(GeoGebra, Desmos), observando cómo la hipérbola se aproxima a estas líneas.:@0.115550:0.517460:0.688632:0.517460:0.688632:0.501748:0.115550:0.501748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aplicaciones prácticas y ejemplos:@0.085435:0.541244:0.339334:0.541244:0.339334:0.524575:0.085435:0.524575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada estudiante tendrá que investigar aplicaciones reales de la hipérbola y sus asíntotas. :@0.085435:0.565028:0.728077:0.565028:0.728077:0.549315:0.085435:0.549315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Algunos ejemplos incluyen: :@0.085435:0.641955:0.289749:0.641955:0.289749:0.626242:0.085435:0.626242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.455420:0.641969:0.459451:0.641969:0.459451:0.626256:0.455420:0.626256:0.000000
• :@0.085422:0.715683:0.093926:0.715683:0.093926:0.699971:0.085422:0.699971:0.000000:0.000000
Óptica::@0.115623:0.715683:0.169667:0.715683:0.169667:0.699014:0.115623:0.699014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 En espejos o lentes donde la trayectoria de la luz sigue propiedades hiperbólicas.:@0.169557:0.715683:0.758858:0.715683:0.758858:0.699971:0.169557:0.699971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.739472:0.093926:0.739472:0.093926:0.723760:0.085422:0.723760:0.000000:0.000000
Antenas::@0.115623:0.739472:0.181840:0.739472:0.181840:0.722803:0.115623:0.722803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Uso en antenas parabólicas y telescopios, donde la señal se refleja y concentra en puntos específicos.:@0.181742:0.739472:0.915155:0.739472:0.915155:0.723760:0.181742:0.723760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.085422:0.763263:0.093926:0.763263:0.093926:0.747550:0.085422:0.747550:0.000000:0.000000
Astronomía: :@0.115623:0.763263:0.211847:0.763263:0.211847:0.746593:0.115623:0.746593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Descripción de órbitas hiperbólicas en trayectorias de cometas.:@0.211728:0.763263:0.669686:0.763263:0.669686:0.747550:0.211728:0.747550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada estudiante puede presentar cómo la comprensión de la hipérbola y sus asíntotas es útil en su aplicación :@0.085417:0.787047:0.918677:0.787047:0.918677:0.771334:0.085417:0.771334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asignada.:@0.085417:0.803688:0.153553:0.803688:0.153553:0.787976:0.085417:0.787976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Problemas de cálculo y graficación colaborativa:@0.085417:0.827472:0.444545:0.827472:0.444545:0.810803:0.085417:0.810803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Creen problemas en los que cada estudiante trabaje en calcular elementos de la hipérbola, como la ubicación de las :@0.085417:0.851256:0.918863:0.851256:0.918863:0.835544:0.085417:0.835544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asíntotas, el centro, o los focos.:@0.085417:0.867898:0.307295:0.867898:0.307295:0.852185:0.085417:0.852185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reúnan los resultados de todos los estudiantes para formar un gráfico completo en una pantalla, mostrando cómo :@0.085417:0.891682:0.919071:0.891682:0.919071:0.875969:0.085417:0.875969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se construye una hipérbola paso a paso.:@0.085417:0.908324:0.375273:0.908324:0.375273:0.892611:0.085417:0.892611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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