What is an equation for the parabola with focus (0, -12) and directrix y = 12

Question

asked Mar 10, 2021 164k views

1 Answer

Izabela Orlowska · Answer 1 · 2021-03-14T11:25:46+0000

Given:

Focus of a parabola is (0, -12) and directrix is y = 12.

To find:

The equation of the parabola.

Solution:

General form of a parabola is

(x-h)^2=4p(y-k) ...(i)

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

Focus is (0, -12).

(h,k+p)=(0,-12)

h=0

k+p=-12 ...(ii)

Directrix is y = 12.

k-p=12 ...(iii)

Adding (ii) and (iii), we get

2k=0

k=0

Putting k=0 in (ii), we get

0+p=-12

p=-12

Putting h=0, k=0 and p=-12 in (i).

(x-0)^2=4(-12)(y-0)

x^2=-48y

-(1)/(48)x^2=y

Therefore, the required equation of parabola is
.