ANSWER
C.
[tex]{(y - 5)}^{2} = 8x [/tex]
EXPLANATION
It was given that, the vertex of the parabola is (0,5).
The directrix of this parabola is x=2.
The directrix tells us that, the parabola will open horizontally in the positive x-axis direction.
Hence the equation of this parabola is of the form;
[tex] {(y - k)}^{2} = 4p(x - h)[/tex]
we plug in the vertex h=0, k=5 to get,
[tex]{(y - 5)}^{2} = 4p(x - 0)[/tex]
p is the distance from the vertex to the directrix, which is
[tex]p = 2 - 0 = 2[/tex]
Hence, we the equation of the parabola becomes,
[tex]{(y - 5)}^{2} = 4 \times 2(x - 0)[/tex]
[tex]{(y - 5)}^{2} = 8x [/tex]
