Question

Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4.

Answer options:
y = 1 /16x2
y^2 = 16x
y^2 = 4x
y = 1/ 4x2

Answer 1

If the focus is at (0,4), and the directrix is at y=-4, the parabola opens upwads, so the standard equation is
\(\large y-k=\frac{(x-h)^2}{4p}\)
where (h,k) is the position of the vertex.
It so happens that the vertex is half-way between the focus and the directrix, and the half distance is p.

Answer 2

So your first step is find (h,k), the point half-way between focus and the directrix.
then substitute in the standard formula and simplify.

Answer 3

It turns out that (h,k)=(0,0) because x=0, y=(4+-4)/2=0. That should make your life a little easier.