A curve has parametric equations $x=\sqrt{2}\cos t$, $y=3\sin t$, for $-\frac{\pi }{2}\le t\le \frac

Question

A curve has parametric equations $x=\sqrt{2}\cos t$, $y=3\sin t$, for $-\frac{\pi }{2}\le t\le \frac{\pi }{2}$. Find the exact area bounded by the curve, the $y$-axis and the line $x=1$. [5] The curve $C$ has an equation ${{y}^{2}}-2y-x=-2$. The region $S$ is bounded by the curve $C$ and the line $y=x-2$. Find the volume of the solid formed when the region $S$ is rotated about the $y$-axis through four right angles. [3]

Accepted Answer

(a) $3\sqrt{2}\left(\dfrac{\pi}{4} + \dfrac{1}{2}\right)$ units$^{2}$; (b) $\dfrac{117\pi}{5}$ units$^{3}$

2017 YIJC Promo Q5

2017 YIJC Promo Q5

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