Question

If the focus of parabola is at $(0,-3)$ and its directrix is $y=3$, then its equation is:

• A. $x^2=-12y$
• B. $x^2=12y$
• C. $y^2=-12y$
• D. $y^2=12x$

Answer 1

The correct option is A $x^2=-12y$

Given, focus $=(0,-3)$ and its direction $y=3$

$P$ is any point on the parabola and $S$ is the focus and $M$ is on the the Directrix such that $PM$ is perpendicular to directrix.
Using definition of parabola
$PS=PM\Rightarrow P{S}^2=P{M}^2$

$\Rightarrow (x-0{)}^2+(y+3{)}^2=(y-3{)}^2$

$\Rightarrow x^2=(y-3{)}^2-(y+3{)}^2=2y(-3-3)=-12y$