A curve $C$ has parametric equations $x=\ln (2t)$, $y={{ an }^{-1}}(2t)$, where $t0$. Describe the

Question

A curve $C$ has parametric equations $x=\ln (2t)$, $y={{	an }^{-1}}(2t)$, where $t>0$. Describe the behaviour of the curve $C$ as $x	o \infty $ and $x	o -\infty $. Sketch $C$, showing clearly the asymptotes and the axial intercepts. [3] Show that the gradient of $C$ at the point where $y=p$ is $\frac{1}{2}\sin 2p$. [3] Hence find the area of triangle bounded by the $x$-axis, the tangent and normal to $C$ when $p=\frac{\pi }{4}$. [5]

Accepted Answer

$\frac{5}{64}\pi^2$ units²

2008 AJC P1 Q12 [Modified]

2008 AJC P1 Q12 [Modified]

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