Question

What is the equation in standard form of the parabola with a focus at (13,0) and a directrix of x= -5?

Answer 1

`(y-0)^2=36(x-4)" "`Vertex Form
or `y^2=36(x-4)`

Explanation:

With the given point `(13, 0)` and directrix `x=-5`, we can calculate the `p` in the equation of the parabola which opens to the right. We know that it opens to the right because of the position of the focus and directrix.

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

From `-5` to `+13`, that is 18 units, and that means the vertex is at `(4, 0)`. With `p=9` which is 1/2 the distance from focus to directrix.

The equation is

`(y-0)^2=36(x-4)" "`Vertex Form
or `y^2=36(x-4)`

God bless....I hope the explanation is useful.