Write an equation for the parabola.
-vertex: $( - 2,5 )$, directrix: $y = 11$
A) $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$
B) $( y + 2 ) ^ { 2 } = 8 ( x - 5 )$
C) $( y + 2 ) ^ { 2 } = - 24 ( x - 5 )$
D) $( x + 2 ) ^ { 2 } = - 24 ( y + 5 )$

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens up or down is $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus or directrix. Given the vertex $(-2, 5)$ and the directrix $y = 11$, the parabola opens downward (since the directrix is above the vertex), and the distance $p = 5 - 11 = -6$. Substituting $h = -2$, $k = 5$, and $p = -6$ into the vertex form gives $(x + 2)^2 = -24(y - 5)$.

Write an Equation for the Parabola (−2,5)( - 2,5 )(−2,5) , Directrix

Write an Equation for the Parabola $( - 2,5 )$ , Directrix