What is an Ellipse? | Geometry, Ellipses Definition, Introduction to Ellipses

What is an ellipse? Ellipses are very interesting shapes, and we will be going over the definition of an ellipse and many related terms in today's geometry math lesson!
An ellipse is defined by three things: two points, each called a focus of the ellipse (collectively called the "foci"), and a distance we will call 2a. The importance of this distance is as follows.
With a distance 2a, and two points F_1 and F_2, the ellipse given by this information is the set of all points such that for each point, the sum of its distances from F_1 and F_2 is equal to 2a. So every point on the ellipse has this property that the sum of its distances from the foci is 2a, the exact same number for every point. It's pretty cool! You might notice some similarity to circle in this definition.
Remember that a circle is the set of all points that are a given distance from a given point, called the radius and center respectively. Ellipses are a generalization of circles, which means that circles are special types of ellipses. An ellipse whose foci are the same point is a circle. All of this information is much better explained with visuals, so check out the video lesson!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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