Question

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

Answer 1

Answer:

$y=-\frac{1}{8}x^2$

Step-by-step explanation:

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

The distance between the focust and the directrix is the value of 2p

Distance beween focus (0,-2) and y=2 is 4

$2p=4, p=2$

The distance between vertex and focus is p that is 2

Focus is at (0,-2) , so the vertex is at (0,0)

General form of equation is

$y-k=-\frac{1}{4p}(x-h)^2$

where (h,k) is the vertex

Vertex is (0,0) and p = 2

The equation becomes

$y-0=-\frac{1}{4(2)}(x-0)^2$

$y=-\frac{1}{8}x^2$

Answer 2

Hello,
The parabola having like focus (0,p/2) and as directrix y=-p/2 has as equation x²=2py

Here -p/2=2==>p=-4

x²=-8y is the equation.