A parabola can be drawn given a focus of (0, 2) and a directrix of y = 0. Write the equation of the parabola in any form.

Question

asked Dec 14, 2021 105k views

1 Answer

Guadalupe · Answer 1 · 2021-12-19T16:02:21+0000

Given:

Focus of a parabola = (0,2)

Directrix: y=0.

To find:

The equation of parabola.

Solution:

The equation of parabola is

y=(1)/(4p)(x-h)^2+k ...(i)

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

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

On comparing both sides, we get

h=0

k+p=2 ...(ii)

On comparing y=k-p and y=0, we get

k-p=0 ...(iii)

Adding (ii) and (iii), we get

2k=2

k=1

Putting k=1 in (ii).

1+p=2

p=2-1

p=1

Putting h=0, k=1 and p=1 in (i).

y=(1)/(4(1))(x-(0))^2+(1)

y=(1)/(4)x^2+1

Therefore, the equation of required parabola is
.