How do you find the equation of a diagonal parabola using the directrix and focus?

directrix is x+y=4
focus is (4,4)
right now i have (x^2)+(y^2)-2xy-8x-8y+48=0

do i need to further simplify this? is it even close to right? my teacher didn't go over this concept at all in class she just threw a few harder problems at the end of the homework to "challenge" us.

((i also have done some work with that and gotten it to (x-4)^2 +(y-4)^2 = 8(y-2) so if that's what i need to change it to..))