A spheroid is an ellipsoid of revolution obtained by rotating an ellipse about a principal axis. Rotation about the shorter axis gives an oblate spheroid; rotation about the longer axis gives a prolate spheroid. Thus the oblate form is a member of the general family.
A prolate spheroid is an ellipsoid with two equal shorter semiaxes and a longer symmetry-axis semiaxis. Its meridional section is an ellipse rotated about its major axis. In the coordinates with , a fixed regular has equatorial radius and polar radius ; its focal separation is independent of , giving a confocal family.
For the prolate spheroid with , intersect the concentric sphere . When , subtraction gives two circles in the perpendicular planesTheir centers lie on the long principal axis and the line through the centers is normal to both planes. At the circles merge into the equator; at they shrink to the two polar vertices. There is no intersection for or .
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A spheroid is a three-dimensional geometric shape that is similar to a sphere but is slightly flattened or elongated along one or more axes. The most common types of spheroids are: 1. **Prolate Spheroid**: This shape is elongated along one axis, meaning it is longer in one direction than in the others. An example of a prolate spheroid is an American football.