A $C$ curve has parametric equations $x={{\mathrm{e}}^{ heta }}\sin heta $, $y={{\mathrm{e}}^{ h

Question

A $C$ curve has parametric equations $x={{\mathrm{e}}^{	heta }}\sin 	heta $, $y={{\mathrm{e}}^{	heta }}\cos 	heta $, where ${-\frac{\pi}{2} Sketch $C$, indicating clearly the axial intercepts. [2] $C$ cuts the $y$- and $x$-axes at points $A$ and $B$ respectively. A particle moves along $C$ from $A$ to $B$, with its $x$-coordinate increasing at a constant rate of $0.1$ units per second. Find the exact rate of change of its $y$-coordinate when $x=\frac{1}{2}{{\mathrm{e}}^{\frac{\pi }{6}}}$. [3] The tangent at the point $P$ on $C$ is parallel to the $y$-axis. Find the equation of this tangent. [4] The point $Q$ on $C$ is such that the angle ${POQ=\frac{\pi }{2}}$. Find the area of triangle $OPQ$. [5]

Accepted Answer

(i) $A=(0,1)$, $B=(e^{\pi/2},0)$ (ii) $\frac{2-\sqrt3}{10}\text{ units/s}$ (iii) $x=-\frac1{\sqrt2}e^{-\pi/4}$ (iv) $\frac12\text{ unit}^2$

2015 VJC P1 Q9

2015 VJC P1 Q9

Video Solution:

Solution:

Solution locked