What is the equation of a parabola with a vertex at (4,8) and a directrix at y=5?

I calculated the distance from the vertex to the directrix as p=3.
my answer key says p=6. I cannot see were I went wrong. Can anyone provide some guidance?

If p=3 is correct then the equation would be:

Focus = (4,11)

(x-h)^2 = 2p(y-k)

(x-4)^2 = 6(y-8)

Thanks in advance!

From what I can see, p=3. The vertex is halfway between the focus and the directrix.

The distance between the focus and the directrix is 6, if they mean that.

One thing, the formula is (x-h)^{2}=4p(y-h), not 2p.

Since p=3, we get 4p=12. What you have looks good, other than that.

I graphed it and here is what I got.