(This page refers to eccentricity in mathematics. For other uses, see the disambiguation page eccentricity.)

In mathematics, eccentricity is a parameter associated with every conic section, see Conic section#Eccentricity. It can be thought of as a measure of how much the conic section deviates from being circular. In particular,

• The eccentricity of a circle is zero.
• The eccentricity of an ellipse is greater than zero and less than 1.
• The eccentricity of a parabola is 1.
• The eccentricity of a hyperbola is greater than 1.
• The eccentricity of a straight line is infinity.

Ellipse

For any ellipse, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b, the eccentricity is given by

The eccentricity is the ratio of the distance between the foci (F₁ and F₂) to the major axis; i.e.

The term linear eccentricity is used for ea.

Hyperbola

For any hyperbola, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b, eccentricity is given by

External links

• MathWorld: Eccentricity