Question

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

Answer 1

A polar graph that is a limacon has a formula similar to `r= a +- bcostheta` or `r= a +- bsintheta`
where `a<b` or `a>b`

Case1: `a<b`
Here you have a limacon with an inner loop
Example: `r = 2 + 4costheta`

Case2: `a>b`
In this case, the limacon does not have an inner loop.
Example: `r = 5 + costheta`