Cardioids and Limacons

These can be split up into the following three cases.

1. Cardioids: r = a + a cos θ and r = a + a sin θ.

These encompass a graph that is vaguely heart shaped and all time contain the origin.

2.   Limacons along with an inner loop : r = a + b cos θ and r = a + b sin θ along with a < b .

These will have an inner loop and will always contain the origin.

3.   Limacons with no an inner loop : r = a + b cos θ and r = a + b sin θ with a > b .

These do not contain an inner loop and do not consist of the origin.