Hyperboloids and Ellipsoids

This Demonstration shows hyperboloids of one and two sheets as well as ellipsoids. When modeling ellipsoids, make the , , and values equal to form a sphere.
The equation for the hyperboloid of one sheet is . The equation for the hyperboloid of two sheets is , and the equation of the ellipsoid is .

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DETAILS

Hyperboloids are obtained by rotating a hyperbola.
An ellipsoid is obtained when a 2D ellipse is rotated around either the semimajor or semiminor axis. However, the ellipsoid formed by rotating an ellipse on its semimajor axis will not be the same as the ellipsoid formed by rotating the ellipse on its semiminor axis. Also, there are ellipsoids that are not formed from the rotation of an ellipse; for example, .
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