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.
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 (x/k)2-(y/R)2=1.
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.
![[alogo]](alogo.png){kind=small}
Pascal's Limacon ![[0_0]](Limacon_files/Limacon_0_0_0.png)
![[0_1]](Limacon_files/Limacon_0_0_1.png)
![[0_2]](Limacon_files/Limacon_0_0_2.png)
![[0_3]](Limacon_files/Limacon_0_0_3.png)
![[1_0]](Limacon_files/Limacon_0_1_0.png)
![[1_1]](Limacon_files/Limacon_0_1_1.png)
![[1_2]](Limacon_files/Limacon_0_1_2.png)
![[1_3]](Limacon_files/Limacon_0_1_3.png)