Values
| conic section | equation | eccentricity (e) | linear eccentricity (c) |
|---|---|---|---|
| circle | |||
| ellipse | |||
| parabola | |||
| hyperbola |
where, when applicable, a is the length of the semi-major axis and b is the length of the semi-minor axis.
When the conic section is given in the general quadratic form
the following formula gives the eccentricity e if the conic section is not a parabola (which has eccentricity equal to 1), not a degenerate hyperbola or degenerate ellipse, and not an imaginary ellipse:
where = 1 if the determinant of the 3×3 matrix
is negative or = -1 if that determinant is positive.
Read more about this topic: Eccentricity (mathematics)
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—Friedrich Nietzsche (1844–1900)