Find the equation in standard form of the parabola described.
-The vertex has coordinates (9, -3), and the focus has coordinates (9, -7).
A) $( y - 3 ) ^ { 2 } = 8 ( x + 9 )$
B) $( x - 9 ) ^ { 2 } = 16 ( y + 3 )$
C) $( y - 3 ) ^ { 2 } = - 8 ( x + 9 )$
D) $( x - 9 ) ^ { 2 } = - 16 ( y + 3 )$

Question

Find the equation in standard form of the parabola described.
-The vertex has coordinates (9, -3), and the focus has coordinates (9, -7). 
A) $( y - 3 ) ^ { 2 } = 8 ( x + 9 )$
B) $( x - 9 ) ^ { 2 } = 16 ( y + 3 )$
C) $( y - 3 ) ^ { 2 } = - 8 ( x + 9 )$
D) $( x - 9 ) ^ { 2 } = - 16 ( y + 3 )$

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 $(9, -3)$ and the focus $(9, -7)$, the parabola opens downward because the focus is below the vertex. The distance $p = 4$, but since the parabola opens downward, we use $-4$ for $p$. Substituting $h = 9$, $k = -3$, and $p = -4$ into the formula gives $(x - 9)^2 = -16(y + 3)$, which matches option D.

Find the Equation in Standard Form of the Parabola Described (y−3)2=8(x+9)( y - 3 ) ^ { 2 } = 8 ( x + 9 )(y−3)2=8(x+9)

Find the Equation in Standard Form of the Parabola Described $( y - 3 ) ^ { 2 } = 8 ( x + 9 )$