Find the equation of a parabola with a focus at (4,–1) and a directrix at y = –3, and graph it on a coordinate plane.

Answer 1

The vertex is 1/2 way between focus and directrix and will open upwards. The vertex point is (4, -2)

This implies that the form of the parabola is 4p(y+2) = (x-4)² where p is the focal length (1/2 of distance from focus to directrix = 1).

4(y+2) = (x-4)²