Question

Identify the focus and directrix of the parabola represented by the equation (y - 2)^2 = -4( x + 2)

Answer 1

Write (y - 2)^2 = 4p(x + 2). Here 4p = -4 so p = -1 and the vertex is (h,k)=(-2,2).

Focus: (h + p, k) = (-2 - 1, 2) = (-3, 2).
Directrix: x = h - p = -2 - (-1) = -1.