Construction and Equations
Let the radius of C be a. By translation and rotation, we may take O to be the origin and the center of the circle to be (a, 0), so A is (2a, 0). Then the polar equations of L and C are:
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By construction, the distance from the origin to a point on the cissoid is equal the difference between the distances between the origin and the corresponding points on L and C. In other words, the polar equation of the cissoid is
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Applying some trigonometric identities, this is equivalent to
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Let in the above equation. Then
are parametric equations for the cissoid.
Converting the polar form to Cartesian coordinates produces
Read more about this topic: Cissoid Of Diocles
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