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La Parábola

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La Parábola

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About this activity

Parábolas: definición y ecuaciones

Created by

LUIS ERIC PAZ BENITES
LUIS ERIC PAZ BENITES
Peru

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La Parábola
 

La ParábolaOnline version

Parábolas: definición y ecuaciones

by LUIS ERIC PAZ BENITES
1

Introducción a la parábola

La parábola es la curva generada por una distancia constante a un foco y a una directriz. Es simétrica respecto a su eje.

2

Definición geométrica

Cada punto equidista del foco y de la directriz forma la parábola. Su eje es la línea de simetría que la divide en dos mitades iguales.

3

Foco y directriz

El foco es un punto interior, y la directriz es una recta. Juntos definen la forma, la distacia focal y la apertura de la parábola.

4

Ecuación en coordenadas

En coordenadas cartesianas, la parábola puede expresarse como y = ax^2 + bx + c. El coeficiente a determina la apertura y orientación.

5

Forma canónica

En forma canónica, la parábola con vértice en (h, k) se escribe como (y-k) = a(x-h)^2, revelando vértice y eje de simetría.

6

Vértice y eje

El vértice es el punto más bajo o alto, según la apertura. El eje es la recta vertical x = h que pasa por el vértice.

7

Lado recta y foco

La distancia focal p define la abertura. Si p>0, la parábola abre hacia arriba; si p<0, abre hacia abajo.

8

Propiedades clave

Propiedades: simetría respecto al eje, apertura constante y vértice que indica la dirección. La distancia focal determina la apertura.

9

Ejemplos prácticos

Una trayectoria parabólica describe el alcance de un objeto proyectado. Las antenas parabólicas enfocan señales hacia el foco.

10

Aplicaciones y resumen

Las parábolas aparecen en óptica, astronáutica y matemáticas. Identifica vértice, foco y ecuación para describir su forma.
 
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