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