Question

How do you write an equation for the parabola with focus (0,2) and directrix y=-2?

Answer 1

`y = 1/8 x^2`

Explanation:

The equation of the parabola with focus and directrix - F(a, b), D(y=c)
is given by:
`(x-a)^2 + b^2 -c^2 = 2y (b-c)`
Now substitute`F(0, 2)` and `D(x, -2) AA x: y(x) = c`
`x^2 = 2y(2-(-2)) = 8y`
`y = 1/8 x^2`