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# Ellipse foci review

Review your knowledge of the foci of an ellipse.

## What are the foci of an ellipse?

The ${\text{foci}}$ of an ellipse are two points whose sum of distances from any point on the ellipse is always the same. They lie on the ellipse's ${\text{major radius}}$ .

The distance between each focus and the center is called the $f$ with the major radius $p$ and the minor radius $q$ :

**focal length**of the ellipse. The following equation relates the focal length*Want to learn more about the foci of an ellipse? Check out this video.*

## Finding the foci of an ellipse

Given the radii of an ellipse, we can use the equation ${f}^{2}={p}^{2}-{q}^{2}$ to find its focal length. Then, the foci will lie on the major axis, $f$ units away from the center (in each direction). Let's find, for example, the foci of this ellipse:

We can see that the major radius of our ellipse is $5$ units, and its minor radius is $4$ units.

The major axis is the horizontal one, so the foci lie ${3}$ units to the right and left of the center. In other words, the foci lie at $(-4\pm {3},3)$ , which are $(-7,3)$ and $(-1,3)$ .

## Check your understanding

*Want to try more problems like this? Check out this exercise and this exercise.*

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