Editing Spheroid (section)

==Equation==
[[File:ellipsoid-rot-ax.svg|thumb|350px| The assignment of semi-axes on a spheroid. It is oblate if {{math|''c'' < ''a''}} (left) and prolate if {{math|''c'' > ''a''}} (right).]]
The equation of a tri-axial ellipsoid centred at the origin with semi-axes {{mvar|a}}, {{mvar|b}} and {{mvar|c}} aligned along the coordinate axes is
:<math>\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2} = 1.</math>

The equation of a spheroid with {{mvar|z}} as the [[symmetry axis]] is given by setting {{math|''a'' {{=}} ''b''}}:
:<math>\frac{x^2+y^2}{a^2}+\frac{z^2}{c^2}=1.</math>

The semi-axis {{mvar|a}} is the equatorial radius of the spheroid, and {{mvar|c}} is the distance from centre to pole along the symmetry axis. There are two possible cases:
* {{math|''c'' < ''a''}}: oblate spheroid
* {{math|''c'' > ''a''}}: prolate spheroid
The case of {{math|''a'' {{=}} ''c''}} reduces to a sphere.