ANSWER
C. is the correct answer
[tex] {y}^{2} = 32x[/tex]
EXPLANATION
The given parabola has a focus at (8,0) and directrix at x=-8.
The equation of this parabola is of the form:
[tex] {y}^{2}=4px[/tex]
Where p is the the distance from the vertex to the focus.
Since the vertex is at the origin,the distance from the vertex to the focus (8,0) is p=8.
[tex] {y}^{2} = 4(8)x[/tex]
[tex] {y}^{2} = 32x[/tex]
