Question

Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half.

Answer choices:

a) f(x) = -(x+2)^2 - 3/4
b) f(x) = (x+2)^2 + 3/4
c) f(x) = -(x-2)^2 + 3/4
d) f(x) = - (x-2)^2 - 3/4

Answer 1

The vertex is a point that is half way between the focus and the directrix. \[\sf \text{focus}: ~(2,-1) \\ \text{directrix}: ~ y=-\frac{1}{2}\]