Exercise 16

Reparametrize the curve \[ \mathbf{r}(t) = \left( \frac{2}{t^2+1} - 1 \right)\mathbf{i} + \frac{2t}{t^2+1}\mathbf{j} \] with respect to arc length measured from the point \((1, 0)\) in the direction of increasing t. Express the reparametrization in its simplest form. What can you conclude about the curve?