Question

If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is

A. x² = –12y
B. x² = 12y
C. y² = –12x
D. y² = 12x

Answer 1

As focus lies on y – axis,

Equation is x² = 4ay or x² = -4ay,

Focus has a –ve co = ordinate, so equation is x² = -4ay,

Co – Ordinate of focus = (0, -a)

-a = -3

a = 3

As per the equation,

x² = -4ay

x² = -4 (3) y

x² = -12y

Hence, the required equation is x² = -12y.

Option (A) is the answer.