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Tschirnhausen Cubic Catacaustic

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TschirnhausenCubicCatacaustic

The catacaustic of the Tschirnhausen cubic with parametric representation

x=3(t^2-3)
(1)
y=t(t^2-3)
(2)

with radiant point at (-8,0) is the semicubical parabola with parametric equations

x_c=6(t^2-1)
(3)
y_c=4t^3
(4)

and Cartesian equation

2(x+6)^3=27y^2.
(5)

See also

Catacaustic, Tschirnhausen Cubic

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References

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

Referenced on Wolfram|Alpha

Tschirnhausen Cubic Catacaustic

Cite this as:

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

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