Write an equation for the parabola.
-vertex $( 3,2 )$, focus $( 3,4 )$
A) $2 ( y - 2 ) = ( x - 3 ) ^ { 2 }$
B) $8 ( y - 2 ) = ( x - 3 ) ^ { 2 }$
C) $y - 2 = 8 ( x - 3 ) ^ { 2 }$
D) $( y - 2 ) ^ { 2 } = 8 ( x - 3 )$

Question

Quizplus · Accepted Answer

The focus and vertex of a parabola provide information about its orientation and dimensions. The vertex is at (3,2), and the focus is at (3,4), indicating the parabola opens upwards. The distance between the vertex and focus, which is 2, is the value of $1/4p$, where $p$ is the distance from the vertex to the focus or directrix. Thus, $4p = 4(2) = 8$. The correct equation, considering the vertex form of a parabola $(x-h)^2 = 4p(y-k)$ for a parabola opening upwards, is $8(y-2) = (x-3)^2$.

Write an Equation for the Parabola (3,2)( 3,2 )(3,2) , Focus (3,4)( 3,4 )(3,4)

Write an Equation for the Parabola $( 3,2 )$ , Focus $( 3,4 )$