2019 DHS Promo Q4
A curve $C$ is defined by the parametric equations
$x=\frac{t}{1+{{t}^{2}}}$, $y=\frac{t}{1-{{t}^{2}}}$, where $0\le t<1$.
(i)
Find the equation of the tangent to $C$ at the point where $x=\frac{2}{5}$.
[4]
(ii)
Find the exact area of the finite region bounded by $C$, the tangent found in part (i) and the $x$-axis.
[4]
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