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Cardioid Negative Pedal Curve

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CardioidNegativePedalCurveCircle

For the cardioid given parametrically as

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

the negative pedal curve with respect to the pedal point (x_0,y_0)=(0,0) is the circle

x_n=a(1+cost)
(3)
y_n=asint.
(4)
CardioidNegativePedalCurveCissoid

For the pedal point (2a,0), the negative pedal curve is a cissoid of Diocles with equation

x_n=-2/3acos(1/2t)^2
(5)
y_n=2/3asin^2(1/2t)tan(1/2t).
(6)

See also

Cardioid, Cardioid Pedal Curve, Negative Pedal Curve

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References

Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 157, 1967.

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Cardioid Negative Pedal Curve

Cite this as:

Weisstein, Eric W. "Cardioid Negative Pedal Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CardioidNegativePedalCurve.html

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