Find the equation in standard form of the parabola described.
-The vertex has coordinates (5, 6), and the focus has coordinates (5, 3).
A) $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$
B) $( x - 5 ) ^ { 2 } = - 12 ( y - 6 )$
C) $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$
D) $( x - 5 ) ^ { 2 } = 12 ( y - 6 )$

Question

Find the equation in standard form of the parabola described.
-The vertex has coordinates (5, 6), and the focus has coordinates (5, 3). 
A) $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$
B) $( x - 5 ) ^ { 2 } = - 12 ( y - 6 )$
C) $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$
D) $( x - 5 ) ^ { 2 } = 12 ( y - 6 )$

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. Since the focus is below the vertex, the parabola opens downward, making $p = -3$. Substituting $h = 5$, $k = 6$, and $p = -3$ into the formula gives $(x - 5)^2 = -12(y - 6)$, which matches option B.

Find the Equation in Standard Form of the Parabola Described (y−6)2=8(x−5)( y - 6 ) ^ { 2 } = 8 ( x - 5 )(y−6)2=8(x−5)

Find the Equation in Standard Form of the Parabola Described $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$