First slide

Parabola

Question

The equation of the parabola having focus at $(0, - 3)$ and directrix $y = 3$

Easy

A

$y^{2} = 24 x$
B

$y^{2} = 12 x$
C

$y^{2} = - 24 x$
D

$x^{2} = - 12 y$

Solution

Focus $(0, - 3)$ and directrix $y = 3$
Since, the focus lies on the $y -$ axis, it is the axis of parabola
Also, the directrix $y = 3$ in the above the $x -$ axis, while the focus $(0, - 3)$ i is below $x -$ axis
hence, the parabola is of the form
$x^{2} = 4 a y H e r e a = 3 T h e r e f o r e, t h e e q u a t i o n o f t h e r e q u i r e d p a r a b o l a i s x^{2} = 12 y$

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