formula

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

Eccentricity =(ra-rp)/(ra+rp), where ra refers to the distance from the far point and rp refers to the distance from the near point.

practical application

Eccentricity of circle =0

Eccentricity of ellipse: e=c/a(0, 1), the closer e is to 0, the more round the ellipse is, the closer e is to 1, the flatter the ellipse is, the closer e is to 1, and the more lines or parabolas there are. (c) half focal length; A, long half axis (ellipse)/real half axis (hyperbola))

Eccentricity of parabola: e= 1

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

In the unified definition of conic curve, the unified polar coordinate equation of conic curve (quadratic noncircular curve) is

ρ=ep/( 1-e×cosθ), where e stands for eccentricity and p is the distance from the focus to the line of sight.

The distance from the focus to the nearest directrix is equal to ex a.

And that contrast relationship between eccentricity and curve shape is synthesize as follows:

E=0, circle

0<e< 1, ellipse

E= 1, parabola

E> 1, hyperbola