Math 1b  Homework Problem 6.3#13

 

Find the length of the loop formed by

Start by tabulating some values to get a feeling for how these equations behave.

 

At the point where the curve intersects itself, there are two different values of t such that

 and ,

that is

 

or

 

Factoring,

 

Since , 

 

And substituting,

 

so  and  are the two times we seek. 

 

Thus the length we want is