Find the equation of the parabola with focus at ( $0,-8)$ and with directrix $y=8$.
A) $y^{2}=32 x$
B) $y^{2}=-32 x$
C) $x^{2}=-32 y$
D) $x^{2}=32 y$

Question

Quizplus · Accepted Answer

The vertex of the parabola is midway between the focus and the directrix, at (0,0). The parabola opens downwards because the focus is below the directrix. The distance from the vertex to the focus is 8, so $4p = 32$ and $p = -8$. The equation is $x^2 = -32y$.

Find the Equation of the Parabola with Focus at 0,−8)0,-8)0,−8) And with Directrix

Find the Equation of the Parabola with Focus at $0,-8)$ And with Directrix