Question

How do you write a standard form of a parabola with given Focus (4, 3) and Directrix y= -3?

Answer 1

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

Explanation:

The standard form of equation of parabola is

`(x-h)^2=4p(y-k)`,

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

As focus is `(4,3)` and directrix is `y=-3`,

we have `h=4` and as `k+p=3` and `k-p=-3`, we have `k=0` and `p=3`.

Hence equation of parabola is `(x-4)^2=4xx3xxy=12y`
graph{((x-4)^2-12y)(y+3)=0 [-5.38, 14.62, -3.92, 6.08]}