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

Answer 1

The focus of parabola (0, -2) and dirctrix at y = 2

The vertical parabola directrix is in the form y = k - p

So required parabola is vertical.

Standard form of vertical parabola is

Where

(h, k + p) = (0, -2)

h = 0

and k + p = -2 ---> (1)

And directrix y = 2

k - p = 2 ---> (2)

Add the equations (1) and (2).

2k = 0

k = 0

Vetex (h, k) = (0, 0)

Substitute k in equation (1).

0 + p = - 2

p = -2

p < 0 then parabola opens downward.

Substitute (h,k) and p in above standard form.

The parabola equation is .