Formulas de Geometria Analitica 2
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Transcript of Formulas de Geometria Analitica 2
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Vectores
Coordenadas de un vector
Módulo
Vector uni tar io
Suma
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Resta
Producto de un vector por un escalar
Producto escalar de vectores
Expresión anal í t ica del producto escalar
Expresión anal í t ica del módulo de un vector
Expresión anal í t ica del ángulo de dos vectores
Expresión anal í t ica de la or togonal idad de dos vectores
Proyección
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Combinación l ineal de vectores
Sistema de referencia
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istancia entre dos puntos
Coordenadas del punto medio
S im!tr ico de un punto
iv is ión de un segmento
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Puntos a l ineados
Coordenadas del bar icentro
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Ecuaciones de la recta
Vector ia l
Param!tr icas
Continua
Pendiente
Punto"pendiente
#eneral
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Expl íc i ta
Canónica o segmentar ia
$ue pasa por dos puntos
Parale las a l e %e &'
Parale las a l e %e &(
Rectas parale las
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Rectas perpendiculares
Posic iones re lat ivas
Secantes
Parale las
Coincidentes
)ngulo *ue forman dos rectas
istancia de un punto a una recta
Ecuaciones de las bisectr ices
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Ecuación de la mediatr i+
Cónicas
Ecuación de la c i rcunferencia
Ecuación reducida
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Ecuación de la e l ipse
Excentr ic idad
Ecuación reducida
e e%e ver t ical
e e %e ,or i+ontal y centro dist into a l or igen
e e%e ver t ical y centro dist into a l or igen
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Ecuación de la ,ip!rbola
Excentr ic idad
-síntotas
Ecuación reducida
. / 0 "c 12 3 y . 0c 12 3
e e %e ver t ical
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./02 1 "c3 y .02 1 c3
e e %e ,or i+ontal y centro dist into a l or igen
Donde - y 4 t ienen s ignos opuestos .
e e%e ver t ical y centro dist into a l or igen
5ip!rbola e*ui látera
-síntotas
,
Excentr ic idad
Refer ida a sus asíntotas
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Ecuación de la parábola
Ecuación reducida de la parábola
e e %es e l de abscisas y de v!r t ice 02 1 23
e e %es e l de ordenadas y de v!r t ice 02 1 23
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Parale la a &' y v!r t ice dist into a l or igen
Parale la a &(1 y v!r t ice dist into a l or igen