Eccentricity (mathematics)

A family of conic sections of varying eccentricity share a focus point $F$ and directrix line $L$ , including an ellipse (red, $e = 1/2$ ), a parabola (green, $e = 1$ ), and a hyperbola (blue, $e = 2$ ). The conic of eccentricity $0$ in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity $\infty$ is an infinitesimally separated pair of lines.
A circle of finite radius has an infinitely distant directrix, while a pair of lines of finite separation have an infinitely distant focus.

In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular:

The eccentricity of a circle is 0.
The eccentricity of a non-circular ellipse is between 0 and 1.
The eccentricity of a parabola is 1.
The eccentricity of a hyperbola is greater than 1.
The eccentricity of a pair of lines is $\infty .$

Two conic sections with the same eccentricity are similar.