Question

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1

Answer 1

From the given information, the parabola is a regular parabola facing up with vertex at (-5, 2).
Required equation is (x + 5)^2 = 4p(y - 2)

But 2 + p = 5 => p = 5 - 2 = 3

Therefore, required equation is (x + 5)^2 = 4(3)(y - 2)
(x + 5)^2 = 12(y - 2)
y - 2 = 1/12 (x + 5)^2
y = 1/12 (x + 5)^2 + 2
f(x) = 1/12 (x + 5)^2 + 2