The curve is ,

Graph :

(1) Draw the coordinate plane.

(2) Graph the curve , .

From the graph :

Consider the value of for which .

Therefore, the solutions of are .

When :

When :

.

When :

.

Therefore the value of lies between and .

.

Length of the loop of the curve .

Substiute the values ,.

Find the length of the curve.

Theorem :

If a curve is described by the parametric equations  and ,  

then the length of the curve is .

Where .

.

The length of the curve is .