Question

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

Short 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-by-step solution

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.