Question

A parabola has a focus of F(−2,6) and a directrix of x=6. The point P(x,y) represents any point on the parabola, while D(6,y), represents any point on the directrix. What is the equation for this parabola?

Answer 1

equation of a parabola: (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p
in this case, the directric is x=6, so the parabola opens sideways, the equation becomes (y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.
h-p=6
h+p=-2
solve: h=2, p=-4
k=6
plug in the h, p, and k values, so the equation is (y-6)²=-16(x-2)