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 = [画像:(r-cost)/(rcost-1)]
(3)
y_n = [画像:((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 CurveExplore with Wolfram|Alpha
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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 CurveCite this as:
Weisstein, Eric W. "Circle Negative Pedal Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircleNegativePedalCurve.html