Find the standard form of the equation of the parabola with a

Question

focus at (0, 2) and a directrix at y = -2.?

Answer 1

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

The vertical parabola has directrix is in y form.

Required parabola is vertcal.

Standard form of vertical parabola is

Where vertex is (h,k) directrix is y = k - p and focus (h, k + p)

Directrix y = - 2

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

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

h = 0

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

Add the equations (1) and (2).

2k = 0

k = 0

Center (h,k) = (0,0)

Substitute k value in equation (2).

0 + p = 2

p = 2

P > 0 , the parabola opens upward.

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

The parabola equation is .