The envelope of a one-parameter family of curves given implicitly by

(1)

or in parametric form by , is a curve which touches every member of the family. For a curve represented by , the envelope is found by solving

(2)

For a curve represented implicitly, the envelope is given by simultaneously solving

			(3)
			(4)

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 33-34, 1972.

Yates, R. C. "Envelopes." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 75-80, 1952.

CITE THIS AS:

Weisstein, Eric W. "Envelope." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Envelope.html