# How do you determine the shape of a limaçon from the polar equation?

Apr 13, 2015

A polar graph that is a limacon has a formula similar to $r = a \pm b \cos \theta$ or $r = a \pm b \sin \theta$
where $a < b$ or $a > b$

Case1: $a < b$
Here you have a limacon with an inner loop
Example: $r = 2 + 4 \cos \theta$

Case2: $a > b$
In this case, the limacon does not have an inner loop.
Example: $r = 5 + \cos \theta$