Find the standard form of the equation of the parabola.
-Focus at $( 9 , - 5 )$, directrix $y = - 15$
A) $( x - 9 ) ^ { 2 } = 20 ( y + 5 )$
B) $( y + 5 ) ^ { 2 } = 20 ( x - 9 )$
C) $( x - 9 ) ^ { 2 } = 20 ( y + 10 )$
D) $( x + 5 ) ^ { 2 } = 20 ( y + 10 )$

Question

Quizplus · Accepted Answer

The vertex of the parabola is midway between the focus and the directrix, at $(9, -10)$. The equation of the parabola with a vertical axis is $(x - h)^2 = 4p(y - k)$, where $p$ is the distance from the vertex to the focus or directrix. Here, $p = 5$, so the equation is $(x - 9)^2 = 20(y + 10)$.

Find the Standard Form of the Equation of the Parabola (9,−5)( 9 , - 5 )(9,−5)

Find the Standard Form of the Equation of the Parabola $( 9 , - 5 )$