A curve $C$ is defined by the parametric equations $x=\frac{t}{1+{{t}^{2}}}$, $y=\frac{t}{1-{{t}^{2}

Question

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

Accepted Answer

(i) $y = \dfrac{125}{27}x - \dfrac{32}{27}$; (ii) $\dfrac{13}{250}$ units$^{2}$

2019 DHS Promo Q4

2019 DHS Promo Q4

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