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.