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Cardioid Catacaustic

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The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x.

CardioidCatacaustic

For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for the cardioid given parametrically as

x=a(1+cost)cost
(1)
y=a(1+cost)sint
(2)

reduces to the nephroid

x_c=1/4[2+3cost-cos(3t)]
(3)
y_c=sin^3t,
(4)

illustrated above.

See also

Cardioid, Catacaustic

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References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 207, 1972.

Referenced on Wolfram|Alpha

Cardioid Catacaustic

Cite this as:

Weisstein, Eric W. "Cardioid Catacaustic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CardioidCatacaustic.html

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