What is the equation of the parabola with a directrix at y = 4 and focus (0, - 4).

Given that the directrix is at y = 4 and the focus is at (0, - 4), then the vertex is at (h, k) = (0, 0).

p is the distance between the vertex and the focus and between the vertex and the directrix = 4 and since the focus is below the directrix, p is negative, i. e. p = - 4

Equation of a parabola is given by (x - h) ^2 = 4p (y - k)

Therefore, the required equation is (x - 0) ^2 = 4 (-4) (y - 0)

x^2 = - 16y

y = - 1/16 x^2