Q. 11 - Calculus

Question

What type of polar curve is named for a heart? For a snail? For a ribbon? 

Step-by-Step Solution

Answer

The polar curve for the heart is cardioid.

The polar curve for the snail is cochleoid.

The polar curve for the ribbon is lemniscate.

Step 1. Given information

The shape of the polar curves are;

Heart, snail and ribbon.

Step 2. Name the given polar curves by their shape.

The polar curve of equation in form of $r=a(1+\cos \theta )$ has a heart like shape and this curve is called as cardioid.

The polar curve of equation in form of $r=\frac{a\sin \theta }{\theta }$ has a snail like shape and this curve is called as cochleoid.

The polar curve of equation in form of $r^2=a^2\cos \left(2\theta \right)$ has a ribbon like shape and this curve is called as lemniscate.

Where $a$ is a real number.