Question

If a parabola's focus is at (3, −5) and the directrix is at y = 1, what is the vertex form of the equation representing this parabola?

Answer 1

(x - h)² = 4p(y - k) is the focus-directrix form, where the focus is (h, k+p), and the directrix is y=k-p, The vertex of this parabola is at (h, k) .
h=3, k+p=-5, k-p=1, so k=-2, p=-3
so (x-3)²=-12(y+2) is the answer.