Is there any way to generate a function whose graph would give a line of finite length?

Question

Is there any way to generate a function whose graph would give a line of finite length?

We know that we can generate functions which give combined graphs of functions by taking $(g (x)-y)(f (x)-y)=0$. Can we get a function which gives a graph of finite lengh?

Answer 1

As your example involves an implicitly defined function, how about the implicit function $$x^2+y^2=1,$$ whose graph is the unit circle?