Find the equation of the parabola with vertex at (1,5)and focus at (-5,5).
A) $( y - 5 ) ^ { 2 } = - 24 ( x - 1 )$
B) $( y - 5 ) ^ { 2 } = 24 ( x - 1 )$
C) $$( y + 5 ) ^ { 2 } = - 24 ( x + 1 )$$
D) $( y + 5 ) ^ { 2 } = 24 ( x + 1 )$
E) $( y - 5 ) ^ { 2 } = 6 ( x - 1 )$

Question

Find the equation of the parabola with vertex at (1,5)and focus at (-5,5). ​
A) $( y - 5 ) ^ { 2 } = - 24 ( x - 1 )$
B) $( y - 5 ) ^ { 2 } = 24 ( x - 1 )$
C) $$( y + 5 ) ^ { 2 } = - 24 ( x + 1 )$$
D) $( y + 5 ) ^ { 2 } = 24 ( x + 1 )$
E) $( y - 5 ) ^ { 2 } = 6 ( x - 1 )$

Quizplus · Accepted Answer

The vertex form of a parabola's equation is $(y-k)^2=4p(x-h)$ for a parabola opening left or right, where (h,k) is the vertex and p is the distance from the vertex to the focus. Here, the vertex is (1,5), and the focus is (-5,5), indicating the parabola opens leftward (since the focus is to the left of the vertex) and $p=6$ (the distance between the vertex and focus). Substituting $h=1$, $k=5$, and $4p=24$ (since $p=6$), we get $(y-5)^2=-24(x-1)$, which matches option A.

Find the Equation of the Parabola with Vertex at (1,5)and (y−5)2=−24(x−1)( y - 5 ) ^ { 2 } = - 24 ( x - 1 )(y−5)2=−24(x−1)

Find the Equation of the Parabola with Vertex at (1,5)and $( y - 5 ) ^ { 2 } = - 24 ( x - 1 )$