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Capricornoid

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Capricornoid

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation

a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0,

where a>0, b>a^2. The curve plotted above corresponds to a=2, b=8.

This curve has a tacnode at the origin and a crunode at (x,y)=(0,a).

See also

Crunode, Links Curve, Quartic Curve, Tacnode

This entry contributed by Margherita Barile

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References

Shikin, E. V. Handbook and Atlas of Curves. Boca Raton, FL: CRC Press, pp. 98-100, 1995.

Cite this as:

Barile, Margherita. "Capricornoid." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Capricornoid.html

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