The pedal curve of a unit circle with parametric equation
(1)
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(2)
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with pedal point is
(3)
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(4)
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The pedal curve with respect to the center is the circle itself (Gray 1997, pp. 119 and 124-135).
If the pedal point is taken on the circumference (and in particular at the point ), the pedal curve is the cardioid
(5)
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(6)
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and otherwise is a limaçon.