Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - \text { axis }$
A) $( y - 5 ) ^ { 2 } = 25 x$
B) $( y - 1 ) ^ { 2 } = 5 ( x - 5 )$
C) $( x + 5 ) ^ { 2 } = 20 ( y + 5 )$
D) $y ^ { 2 } = 20 x$
E) $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$

Question

Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - \text { axis }$ 
A) $( y - 5 ) ^ { 2 } = 25 x$
B) $( y - 1 ) ^ { 2 } = 5 ( x - 5 )$
C) $( x + 5 ) ^ { 2 } = 20 ( y + 5 )$
D) $y ^ { 2 } = 20 x$
E) $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$

Quizplus · Accepted Answer

Since the directrix is the $y$-axis, the parabola is symmetric around a vertical line. This means the equation will be of the form $(y-k)^2=4p(x-h)$ where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the directrix. Since the vertex is $(5,5)$, we have $(h,k)=(5,5)$. Since the directrix is the $y$-axis, $p$ is the distance from $(5,5)$ to the $y$-axis, which is $5$.

Thus, the equation of the parabola is $(y-5)^2=4\cdot 5(x-5)$, or equivalently, $(y-5)^2=20(x-5)$. Therefore, the answer is $\boxed{	ext{(E)}}$.

Find an Equation for the Parabola with Vertex (5,5)( 5,5 )(5,5)

Find an Equation for the Parabola with Vertex $( 5,5 )$