Q. 12 - Calculus

Question

What is the difference between a cardioid and a limacon? 

Step-by-Step Solution

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 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.