Find an equation for the parabola described.
-Vertex at (6, 1); focus at (6, 3)
A) $( y - 1 ) ^ { 2 } = - 12 ( x - 6 )$
B) $( y - 1 ) ^ { 2 } = 12 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = 8 ( y - 1 )$
D) $( x - 6 ) ^ { 2 } = - 8 ( y - 1 )$

Question

Find an equation for the parabola described.
-Vertex at (6, 1); focus at (6, 3) 
A) $( y - 1 ) ^ { 2 } = - 12 ( x - 6 )$
B) $( y - 1 ) ^ { 2 } = 12 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = 8 ( y - 1 )$
D) $( x - 6 ) ^ { 2 } = - 8 ( y - 1 )$

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. Here, the vertex is at (6, 1) and the focus is at (6, 3), indicating the parabola opens upwards and $p = 2$. Substituting $h = 6$, $k = 1$, and $p = 2$ into the formula gives $(x - 6)^2 = 8(y - 1)$.

Find an Equation for the Parabola Described (y−1)2=−12(x−6)( y - 1 ) ^ { 2 } = - 12 ( x - 6 )(y−1)2=−12(x−6)

Find an Equation for the Parabola Described $( y - 1 ) ^ { 2 } = - 12 ( x - 6 )$