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# 6.1: Equation of an Ellipse

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

Cone

A cone is a solid three-dimensional figure with a circular base and one vertex.

Conic

Conic sections are those curves that can be created by the intersection of a double cone and a plane. They include circles, ellipses, parabolas, and hyperbolas.

Eccentricity

The eccentricity of a conic section is a measure of how much the conic section deviates from being circular. The eccentricity of circles is 0, the eccentricity of ellipses is between 0 and 1, the eccentricity of parabolas is 1, and the eccentricity of hyperbolas is greater than 1. For ellipses and hyperbolas, $e=\frac{c}{a}$.

Ellipse

Ellipses are conic sections that look like elongated circles. An ellipse represents all locations in two dimensions that are the same distance from two specified points called foci.

Ellipses

Ellipses are conic sections that look like elongated circles. An ellipse represents all locations in two dimensions that are the same distance from two specified points called foci.

Foci

The foci of an ellipse are the two points that define the ellipse. The sum of the distances from any point on the ellipse to the foci is constant.

Major Axis

The major axis of an ellipse is the longest diameter of the ellipse.

minor axis

The minor axis of an ellipse is the shortest diameter of the ellipse.

standard form

The standard form of an ellipse centered at $(h,k)$ is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$.

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