Question

what is the equation of the quadratic graph with a focus of (-1,4) and a directrix of y=2? hint: y=a(x-h)^2+k, a=1/4p

Answer 1

y = 1/4(x + 1)^2 + 3.

Explanation:

The general form is (x - h)^2 = 4p(y - k) where the focus is (h, k+p) and the directrix is y = k-p

So we have h = -1

k + p = 4

k - p = 2 Adding:

2k = 6 so k = 3 and p = 1.

Therefore:

(x + 1)^2 = 4(y - 3)

4y = (x + 1)^2 + 12

y = 1/4(x + 1)^2 + 3.