Question

Find the equation of the parabola that satisfies the following conditions :

Focus $(0,-3)$ and Directrix $y=3.$

Answer 1

Focus = (0,-3), Directrix y =3

Since the focus lies on the Y-axis, the Y-axis is the axis of parabola.

Therefore, equation of the parabola is either of the form $x^2=4ay$ or $x^2=-4ay$

Directrix, $y=3$ is above the X-axis, while the focus $(0,-3)$ is below the X-axis.

Hence, the parabola is of the from $x^2=-4ay$

Here, $a=3$

Thus, the equation of the parabola is $x^2=-12y$.