Write an equation for the parabola.
-vertex $( - 5 , - 12 )$, focus $( - 5 , - 14 )$
A) $( x - 5 ) ^ { 2 } = - 56 ( y - 12 )$
B) $8 ( y - 5 ) = ( x - 12 ) ^ { 2 }$
C) $( x + 5 ) ^ { 2 } = - 8 ( y + 12 )$
D) $8 ( y - 12 ) = ( x - 5 ) ^ { 2 }$

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. Given the vertex $(-5, -12)$ and the focus $(-5, -14)$, the parabola opens downward (since the focus is below the vertex), and $p = -2$ (the distance in the y-direction from the vertex to the focus). Substituting $h = -5$, $k = -12$, and $p = -2$ into the vertex form gives $(x + 5)^2 = -8(y + 12)$, which matches choice C.

Write an Equation for the Parabola (−5,−12)( - 5 , - 12 )(−5,−12)

Write an Equation for the Parabola $( - 5 , - 12 )$