Write an equation for the parabola.
-vertex $( 9 , - 10 )$, focus $( 9 , - 6 )$
A) $( x - 9 ) ^ { 2 } = 16 ( y + 10 )$
B) $( y + 10 ) ^ { 2 } = 16 ( x - 9 )$
C) $16 ( y - 10 ) = ( x + 9 ) ^ { 2 }$
D) $y - 10 = 16 ( x + 9 ) ^ { 2 }$

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. Here, the vertex is $(9, -10)$ and the focus is $(9, -6)$, indicating the parabola opens upwards and $p = 4$. Substituting $h = 9$, $k = -10$, and $p = 4$ into the equation gives $(x - 9)^2 = 16(y + 10)$.

Write an Equation for the Parabola (9,−10)( 9 , - 10 )(9,−10)

Write an Equation for the Parabola $( 9 , - 10 )$