Question

.Find the standard form of the equation of the parabola with focus(8,-2) and directrix x=4

Answer 1

well, you know that the parabola

y^2 = 4px

has
vertex at (0,0)
focus at x=p
directrix at x = -p

The vertex is halfway between the focus and the directrix, at (6,-2)

So, shift it right 6, down 2.
Then note that the distance from the focus to the directrix is 8-4=4=2p, and you have p=2. That means the equation is

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

Confirm this at

http://www.wolframalpha.com/input/?i=parabola+(y%2B2)%5E2+%3D+8(x-6)