Eccentricity

Mathematical definition

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Eccentricity（ eccentricity ）, also called Eccentricity , the unified definition is Conic curve Middle, the distance from the moving point to the focus and the distance from the moving point to Guide line The distance ratio of.

Chinese name: Eccentricity
Foreign name: eccentricity

Alias: Eccentricity 、 Eccentricity
Definition: In conic curve, the ratio of the distance from the moving point to the focus and the distance from the moving point to the guide line

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A measure of the flatness of an ellipse. Eccentricity is defined as the ratio of the distance between two focal points of an ellipse and the length of its major axis.

Eccentricity=(ra rp)/(ra+rp), ra refers to Far point Distance, rp means Proximal point Distance.

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Eccentricity of circle=0

Eccentricity of ellipse: e=c/a ∈ (0,1), the closer e is to 0, the rounder the ellipse is, the rounder e equals 0, the more e is to 1, the flatter the ellipse is, and e equals 1, the line segment or parabola 。（c, Half focal length ； a. Long semi axis (ellipse)/real semi axis（ hyperbola ) ）

parabola Eccentricity of: e=1

Eccentricity of hyperbola: e=c/a (1,+∞) (c, semi focal length; a, long semi axis (ellipse)/real semi axis (hyperbola))

stay Conic curve In the unified definition, the unification of conic curve (quadratic non-circular curve) Polar equation by

ρ= ep/(1-e×cos θ)， Where e is eccentricity and p is focus to Guide line Distance.

The distance from the focus to the nearest guide line is equal to ex ± a.

And the correlation between eccentricity and curve shape is summarized as follows:

E=0, circle;

0 ＜ e ＜ 1, ellipse;

e=1, parabola ;

e＞1, hyperbola .

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