Question

Vertex (3,2)
focus(-3,2)

Answer 1

since you give only one focus, I assume it's a parabola. Since both points lie on the line y=2, the parabola opens horizontally. Recall that

y^2 = 4px

has focus at (p,0) and vertex at (0,0)

Your parabola has obviously been shifted up by 2, so it will be

(y-2)^2 = 4px

Your vertex has been shifted right by 3, so

(y-2)^2 = 4p(x-3)

p is the distance from the vertex to the focus, in this case 6, so we have

(y-2)^2 = 24(x-3)

But since the focus is to the left of the vertex, the parabola opens to the left, and we are left with

(y-2)^2 = -24(x-3)

http://www.wolframalpha.com/input/?i=parabola+(y-2)%5E2+%3D+-24(x-3)