Find the standard form of the equation of the parabola with the given characteristics.
Vertex: $( 6,5 )$ ;focus: $( 8,5 )$
A) $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$
B) $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$
D) $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$
E) $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$

Question

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 6,5 )$ ;focus: $( 8,5 )$ ​
A) $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$
B) $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$
D) $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$
E) $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$

Quizplus · Accepted Answer

The standard form of a parabola with a horizontal axis 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 $(6,5)$ and the focus is $(8,5)$, indicating a horizontal parabola with $p=2$. Thus, the equation is $(y-5)^2=8(x-6)$.

Find the Standard Form of the Equation of the Parabola (6,5)( 6,5 )(6,5)

Find the Standard Form of the Equation of the Parabola $( 6,5 )$