Question

What is the equation of a parabola with a directrix x = 8 and focus (-8, 0).

Answer 1

The mid point between the focus and directrix of a parabola is its vertex, namely (0,0).
Since the focus is to the right of the vertex, the parabola has a horizontal axis, namely of the form
\[x=y^2/4c\]
where c=distance between focus and vertex = -8
The equation can also be put as
\[y^2=4cx\]

I am sure you are able to figure out the equation of the parabola