[alogo] Pascal's Limacon

Pascal's Limacon as a pedal of the circle (radius k, a: distance of O from center of the circle).
Here its polar equation and a description in implicit form.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]

The picture shows also the hyperbola
k2(x2+y2)=(R2-ax)2, with R2=a2-k2,
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

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.

See Also



Briot and Bouquet Elements of Analytical Geometry Werner School book company, New York 1896, p. 26

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