An ellipse is a sort of squashed circle, sometimes referred to as an oval.

**Definition of an Ellipse**

Take two points. (Each one is a *focus;* together, they are the *foci.*) An ellipse is the set of all points in a plane that have the following property: the distance from the point to one focus, *plus* the distance from the point to the other focus, is some constant.

They just keep getting more obscure, don’t they? Fortunately, there is an experiment you can do, similar to the circle experiment, to show why this definition leads to an elliptical shape.

**Experiment: Drawing the Perfect Ellipse**

- Lay a piece of cardboard on the floor.
- Thumbtack one end of a string to the cardboard.
- Thumbtack the other end of the string, elsewhere on the cardboard. The string should not be pulled taut: it should have some slack.
- With your pen, pull the middle of the string back until it is taut.
- Pull the pen all the way around the two thumbtacks, keeping the string taut at all times.
- The pen will touch every point on the cardboard such that the distance to one thumbtack, plus the distance to the other thumbtack, is exactly one string length. And the resulting shape will be an ellipse. The cardboard is the “plane” in our definition, the thumbtacks are the “foci,” and the string length is the “constant distance.”

Do ellipses come up in real life? You’d be surprised how often. Here is my favorite example. For a long time, the orbits of the planets were assumed to be circles. However, this is incorrect: the orbit of a planet is actually in the shape of an ellipse. The sun is at one focus of the ellipse (*not* at the center). Similarly, the moon travels in an ellipse, with the Earth at one focus.

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