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Isoptic Curve

For a given curve $C$, consider the locus of the point $P$ from where the Tangents from $P$ to $C$ meet at a fixed given Angle. This is called an isoptic curve of the given curve.

Curve Isoptic
Cycloid curtate or prolate Cycloid
Epicycloid Epitrochoid
Hypocycloid Hypotrochoid
Parabola Hyperbola
Sinusoidal Spiral Sinusoidal Spiral

See also Orthoptic Curve


Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 58-59 and 206, 1972.

Yates, R. C. ``Isoptic Curves.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 138-140, 1952.

© 1996-9 Eric W. Weisstein