Question

How do you write the equation of the parabola in vertex form given focus at (-2,0) and a directrix at x=2?

Answer 1

See the explanation below.

Explanation:

First, plot the point (-2,0) and graph the line x = 2. The center is exactly in between these two, so the center is (0,0).

After finding the center, you must find the value of `p`, which is the distance from the center to the focus. In this case, `p = -2`.

Now you must determine whether the parabola will face right or left. Parabolas always "enclose" the focus, so the parabola here faces left.

The standard form of a sideways parabola is `y^2 = 4px`. Substitute `-2` for `p`.

The equation is `y^2=-8x`.