Question:
Find the equation of the parabola with focus $F(0,-3)$ and directrix $y=3$.
Solution:
Given equation of directrix : y = 3
- $y-3=0$
Above equation is of the form, y - a = 0
Focus of the parabola $F(0,-3)$ is of the form $F(0,-a)$
Therefore, a = 3
For directrix with equation $y-a=0$ and focus $(0,-a)$, equation of the parabola is,
$x^{2}=-4 a y$
$\cdot x^{2}=-12 y$
