A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an orthogonal coordinate system known as confocal ellipsoidal coordinates (Hilbert and Cohn-Vossen 1999, pp. 22-23).
The planes of symmetry of the tangent cone from any point 
in space to any surface of the confocal system which does
not enclose 
are the tangent planes at 
to the three surfaces of the system that pass through 
. As a limiting case, this result means
that every surface of the confocal system when viewed from a point lying on a focal
curve and not enclosed by the surface looks like a circle with its center on the
line of sight, provided that the line of sight is tangent to the focal curve (Hilbert
and Cohn-Vossen 1999, p. 24).
See also
Confocal Ellipsoidal Coordinates, Ellipsoid, Hyperboloid, Quadratic Surface
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References
Hilbert, D. and Cohn-Vossen, S. "The Thread Construction of the Ellipsoid, and Confocal Quadrics." ยง4 in Geometry and the Imagination. New York: Chelsea, pp. 19-25, 1999.
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Cite this as:
Weisstein, Eric W. "Confocal Quadrics." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConfocalQuadrics.html