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Eccentricity (mathematics)

For the eccentricity of a vertex in a graph, see Eccentricity (graph theory).
A family of conic sections of varying eccentricity share a focus point and directrix line, 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 ∞ 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 an ellipse which is not a circle 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

Two conic sections with the same eccentricity are similar.

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