This is what i have done
x^2/a^2 - y^2/b^2 = 1
then i substituted a as 0 and b as 16 and it got me nowhere
I'm guessing it has to be located at 0 but i don't know how to prove it all i know are these equations...
x^2/a^2 - y^2/b^2 = 1, a^2 +b^2 = c^2 and that's all
(P.S. Latex is hard to learn)

The equation for a parabola in this orientation is:

[tex]y^2 = 4px[/tex] where A = (0,0) is the origin and p is the distance from the origin to the focus. The points B = (16, 16), C = (16, -16) are on the parabola. That will enable you to solve for p.