Write an equation for the parabola.
-vertex $( 7 , - 6 )$, focus $( 10 , - 6 )$
A) $( x - 7 ) ^ { 2 } = 12 ( y + 6 )$
B) $x - 7 = 3 ( y + 6 ) ^ { 2 }$
C) $( y + 6 ) ^ { 2 } = 12 ( x - 7 )$
D) $\frac { 3 } { 4 } ( x - 7 ) = ( y + 6 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens horizontally is $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus. Here, the vertex is $(7,-6)$ and the focus is $(10,-6)$, indicating the parabola opens to the right and $p=3$. Substituting $h=7$, $k=-6$, and $p=3$ into the formula gives $(y+6)^2=12(x-7)$.

Write an Equation for the Parabola (7,−6)( 7 , - 6 )(7,−6)

Write an Equation for the Parabola $( 7 , - 6 )$