Question

The limaçon is a polar curve of the form
r=b+acos(t)
If b>=2a, the limaçon is convex. If 2a>b>a, the limaçon is dimpled.
can someone explain why

Answer 1

if \(a =0\)

\(r=b\) , circles centered at the origin

if \(b =0\)

\(r=a\cos(\theta)\) , circles tangental to the origin

adding these together we get the
Limaçon
\[r=b+a\cos(\theta)\]