First slide

Parabola

Question

$The equation of the parabola having focus at (6, 0) a n d d i r e c t r i x a t x = - 6$

Easy

A

$y^{2} = 24 x$
B

$y^{2} = 12 x$
C

$x^{2} = 24 y$
D

$x^{2} = 12 y$

Solution

$Given focus (6, 0), d i r e c t r i x x = - 6$
$S i n c e t h e f o u c s l i e s o n x - a x i s, i t i s t h e a x i s o f p a r a b o l a$
$T h e d i r e c t r i x l i e s i n t h e l e f t s i d e o f t h e y - a x i s$
$H e n c e, t h e p r a b o l a i s i n t h e s t a n d a r d f o r m a s y^{2} = 4 a x$
$A n d d i s t a n c e b e t w e e n f o c u s a n d d i r e c t r i x i s 2 a, H e r e 2 a = 12 H e n c e a = 6$
$T h e r e f o r e, t h e e q u a t i o o n o f t h e p a r a b p l a i s y^{2} = 24 x$

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