The focus of a parabola is located at (0,-2). The directrix of the parabola is represented by y = 2. Which equation represents the parabola?

y2 = - 2x

x2 = - 2y

y2 = - 8x

x2 = - 8y

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

We know that the focus is (0, - 2) which results in h=0 and k+p=-2.

We also know that t he directrix of the parabola is represented by y = 2 so k-p=2

k-p=2

k+p=-2

If we add those 2 equations:

2k=0

k=0

p=-2

Know we replace in the standard form:

(x-0) ^2 = 4 * (-2) * (y-0)

x^2 = - 8*y