# Parabola focus & directrix review

CCSS Math: HSG.GPE.A.2

Review your knowledge of the focus and directrix of parabolas.

## What are the focus and directrix of a parabola?

Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the

**focus**) is equal to their distance from a certain line (the**directrix**).*Want to learn more about focus and directrix of a parabola? Check out this video.*

## Parabola equation from focus and directrix

Given the focus and the directrix of a parabola, we can find the parabola's equation. Consider, for example, the parabola whose focus is at $(-2,5)$ and directrix is $y=3$. We start by assuming a general point on the parabola $(x,y)$.

Using the distance formula, we find that the distance between $(x,y)$ and the focus $(-2,5)$ is $\sqrt{(x+2)^2+(y-5)^2}$, and the distance between $(x,y)$ and the directrix $y=3$ is $\sqrt{(y-3)^2}$. On the parabola, these distances are equal:

*Want to learn more about finding parabola equation from focus and directrix? Check out this video.*