Question

Find the equation of the parabola that satisfies the following conditions: Focus $(0,-3)$; directrix $y=3$

Answer 1

Focus $S=(0,-3)$; directrix $y=3$
Since, the focus lies on the $y$-axis and directrix $y=3$ is above the $x$-axis.
So, the axis of the parabola is $y$-axis.
Therefore, the equation of the parabola is either of the form $x^2=-4ay$
Here $a=3$
Thus, the equation of the parabola is $x^2=-12y$