How do you find the equation of the parabola whose focus is at (3, 3) and whose directrix is at x = 7?

1 Answer
Mar 13, 2018

-8(x-5)=(y-3)^2

Explanation:

A quadratic relation (or function) can be in the form:

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

Since our diretrix is a vertical line, our parabola is horizontal.

We, therefore, use the form 4p(x-h)=(y-k)^2

In this form, the focus is at (h+p,k) and the diretrix is at x=h-p

Using our information, the focus is at (3,3) and the diretrix is at x=7.

Therefore, k=3, h+p=3, and h-p=7

We add the second and the third equations to get:

2h=10

=>h=5 You could use this to find that p=-2

Let's plug in what we know:

4*-2(x-5)=(y-3)^2

=>-8(x-5)=(y-3)^2