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

Answer 1

The parabola with focus (0,6) and directrix y = - 6

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, 6)

h = 0 and k + p = 6 ---> (1)

The x coordinate of vertex is 0.

And directrix y = -6

k - p = -6  ---> (2)

Add the equations (1) and (2).

2k = 0

k = 0

y coorinate of vertex is 0.

(h, k) = (0,0)

Substitute value of k in equation (1).

0 + p = 6

p = 6

p > 0, the parabola opens upward.

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

The parabola equation is .