Question

The focus of the parabola is (0, –3) and and directrix is y = 3, then its equation is
(a) x² = –12y
(b) x² = 12y
(c) y² =–12x
(d) y² = 12x

Answer 1

since focus of the parabola is (0, −3) i.e. y-axis.
Equation of the parabola is either x² = 4ay or x² = −4ay
Now since focus has negative co-ordinate
⇒ equation is of the form x² = – 4ay
∴ Co-ordinate of focus (0, −a) = (0, −3)
⇒ a = 3 for which, equation of parabola,
x² = −4ay
i.e. x² = −4(3)y
i.e. x² = −12y

Hence, the correct answer is option A.