State a sequence of transformations that will transform the circle with equation \({{x}^{2}}+{{y}^{2

Question

State a sequence of transformations that will transform the circle with equation ${{x}^{2}}+{{y}^{2}}=1$. State a sequence of transformations that will transform the circle with equation $\frac{{{\left( x-2 \right)}^{2}}}{9}+{{y}^{2}}=1$.[2] A curve $C$ with cartesian equation $y=\frac{x}{\sqrt{5-{{x}^{2}}}}$ is shown below. $R$ is the finite region enclosed by $C$, the $x$-axis and the line $x=1$. Find the exact area of $R$.[3] Find the exact volume of the solid formed when $R$ is rotated through $2\pi $ radians about the $y$-axis.[6]

Accepted Answer

(a) 1. Scaling parallel to the $x$-axis by a factor of $3$. 2. Translation of $2$ units in the positive direction of the $x$-axis. (b)(i) $(\sqrt{5} - 2)$ units$^2$ (ii) $\left(5\pi\tan^{-1}\left(\frac{1}{2}\right) - 2\pi\right)$ units$^3$

2023 TJC Promo Q9

2023 TJC Promo Q9

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