Question

find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

Answer 1

From the given information, the parabola is a regular parabola facing up with vertex at the origin.
Required equation is (x - 0)^2 = 4p(y - 0)

But 0 + p = 6 => p = 6

Therefore, required equation is x^2 = 4(6)y
x^2 = 24y
y = 1/24 x^2