$\text { Find an equation of the parabola with vertex } ( 0,8 ) \text { and directrix } y = - 3 \text {. }$
A) $y ^ { 2 } = 44 ( x - 8 )$
B) $x ^ { 2 } = 44 ( y - 8 )$
C) $x ^ { 2 } = 44 ( y + 8 )$
D) $x ^ { 2 } = 22 ( y - 8 )$
E) $y ^ { 2 } = 22 ( x - 8 )$

Question

$\text { Find an equation of the parabola with vertex } ( 0,8 ) \text { and directrix } y = - 3 \text {. }$ 
A) $y ^ { 2 } = 44 ( x - 8 )$
B) $x ^ { 2 } = 44 ( y - 8 )$
C) $x ^ { 2 } = 44 ( y + 8 )$
D) $x ^ { 2 } = 22 ( y - 8 )$
E) $y ^ { 2 } = 22 ( x - 8 )$

Quizplus · Accepted Answer

The vertex form of a parabola that opens up or down is $x^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus or directrix. Here, the vertex is $(0, 8)$ and the directrix is $y = -3$, so the parabola opens upwards, and the distance $p$ is $8 - (-3) = 11$. Thus, the equation is $x^2 = 4(11)(y - 8)$ or $x^2 = 44(y - 8)$.

Find an equation of the parabola with vertex (0,8) and directrix y=−3. \text { Find an equation of the parabola with vertex } ( 0,8 ) \text { and directrix } y = - 3 \text {. } Find an equation of the parabola with vertex (0,8) and directrix y=−3.

$\text { Find an equation of the parabola with vertex } ( 0,8 ) \text { and directrix } y = - 3 \text {. }$