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Circle Negative Pedal Curve


CircleNegativePedalCurve
Circle negative pedal curve

For a unit circle with parametric equations

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

the negative pedal curve with respect to the pedal point (r,0) is

x_n=(r-cost)/(rcost-1)
(3)
y_n=((r^2-1)sint)/(rcost-1).
(4)

Therefore if the point is inside the circle (r<1), the negative pedal is an ellipse, if r=1, it is a single point, if the point is outside the circle (r>1), the negative pedal is a hyperbola.


See also

Circle, Ellipse Negative 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.

Referenced on Wolfram|Alpha

Circle Negative Pedal Curve

Cite this as:

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

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