Eccentricity (Mathematics)

(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,

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
e = \sqrt{1-\frac{b^2}{a^2}}.
The eccentricity is the ratio of the distance between the foci (F_1 and F_2) to the major axis; i.e. \left ( \frac{\overline{F_1F_2}}{\overline{AB}} \right ). 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
e = \sqrt{1+\frac{b^2}{a^2}}.

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