Here its polar equation and a description in implicit form.

The picture shows also the hyperbola

k

which is the inverse of the limacon with respect to the circle (c) centered at O (origin) with radius R.

The center of the hyperbola is A and one of the focus is at the origin O.

The hyperbola is the translation by A(a,0) of the one with equation

(x/k)

From the right-angled triangle OAD follows that the limacon is also generated in the following way:

For every point D on the circle with diameter OA, extend OD by a segment of fixed length OB = OB' = k.

Points B,B' describe a limacon.

See Limacon2.html for another way to generate this curve.

Limacon2.html

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