Question

What is the difference between a cardioid and a limacon?

Short answer

The graph of equation $$\begin{gathered} r=a\pm b\cos \theta \\ r=a\pm b\sin \theta \end{gathered}$$is limacon if $\left|\frac{a}{b}\right|\ne 1$

If $\left|\frac{a}{b}\right|=1$then the equation represents a cardioid.

Step-by-step solution

Step 1. Given information

Two polar curves: Cardioid and limacon.

Step 2. The difference between the cardioid and limacon.

The graph of equation $$\begin{gathered} r=a\pm b\cos \theta \\ r=a\pm b\sin \theta \end{gathered}$$is limacon if $\left|\frac{a}{b}\right|\ne 1$

If $\left|\frac{a}{b}\right|=1$then the equation represents a cardioid.

For example $r=2+2\cos \theta$is a cardioid.

$r=1+2\cos \theta$is a limacon.

Limacon has a snail-like shape while cardioid has a heart like shape.