Write an equation for the parabola.
-vertex $( 9 , - 4 )$, focus $( 9,2 )$
A) $( x - 9 ) ^ { 2 } = 24 ( y + 4 )$
B) $24 ( y - 4 ) = ( x + 9 ) ^ { 2 }$
C) $( \mathrm { y } + 4 ) ^ { 2 } = 24 ( \mathrm { x } - 9 )$
D) $y - 4 = 24 ( x + 9 ) ^ { 2 }$

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. Given the vertex $(9, -4)$ and the focus $(9, 2)$, the distance $p = 2 - (-4) = 6$. Since the parabola opens upwards (the y-coordinate of the focus is greater than that of the vertex), we use the formula with $4p = 24$. Substituting $h = 9$, $k = -4$, and $4p = 24$ into the formula gives $(x - 9)^2 = 24(y + 4)$.

Write an Equation for the Parabola (9,−4)( 9 , - 4 )(9,−4)

Write an Equation for the Parabola $( 9 , - 4 )$