Reparametrize the curve r (t) = ( 2 t^2 + 1 - 1 ) i + 2t t^2 + 1 j with respect to…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

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?