The diagram shows the sketch of the curve $C$, ${{\left( y-1 \right)}^{2}}=x\sqrt{{{x}^{2}}-1}$, wit

Question

The diagram shows the sketch of the curve $C$, ${{\left( y-1 \right)}^{2}}=x\sqrt{{{x}^{2}}-1}$, with the vertex at $\left( 1,1 \right)$. Write down the equation of the graph when $C$ is translated $1$ unit in the negative $y$-direction. [1] The shaded region $R$, bounded by $C$ and the vertical line, $x=a$, is rotated through $\pi $ radians about the line $y=1$. By using the substitution $u=\sqrt{{{x}^{2}}-1}$, or otherwise, find the exact volume obtained in terms of $a$. [5]

Accepted Answer

(i) $y^2=x\sqrt{x^2-1}$; (ii) $\frac\pi3(a^2-1)^{3/2}\text{ units}^3$

2013 RVHS Promo Q3

2013 RVHS Promo Q3

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