Question

Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.

Answer 1

May be you should ask @Directrix =P

Jokes apart, one thing to know is that the vertex of a parabola is half-way between the focus and the directrix. This means the x-value of the vertex (the point where the parabola turns) of the parabola is the same as the focus and the directrix (a straight line), also has a point on it with the same x-value.

Since the focus is at (0, 2) and directrix is y = -2, then the point where both of these have the same x-value will be at (0, 2) for the focus and (0, -2) for the directrix. The vertex will also have the same x-value so it will be (0, y). I don't know what the y-value of the vertex is, but I know that it's y-value is half-way between the y-value of the focus, and the y-value of the directrix at x = 0. Directrix y-value is -2 at x = 0 and for the focus it's 2 at x = 0. Halfway between y = -2 and y = 2 is y = 0. So the vertex of the parabola occurs at (0, 0).

So that's x^2 = 4ay = 4(2)y = 8y. Rearranging gives: y = 1/8*x^2

Answer 2

@ballerinaxbb

Answer 3

Thank you so much! Great explanation