Determine an equation for the parabola with focus (7,-2) and directrix y=4.

Answer 1

If I do a sketch and graph the directrix and for focus, I can figure out the vertex is (7,1) It is half way between them.

The vertex form of the parabola is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. Plugging in h and k you get

f(x) = a(x - 7)² + 1

Since the focus is below the directrix, this parabola has to open down. So this means a = -1.

f(x) = - (x - 7)² + 1