A curve with equation $\frac{{{\left( x-2 \right)}^{2}}}{4}+{{y}^{2}}=1$ undergoes, in succession,

Question

A curve with equation $\frac{{{\left( x-2 \right)}^{2}}}{4}+{{y}^{2}}=1$ undergoes, in succession, the following transformations: A: $ \qquad $ A stretch with scale factor $\frac{1}{2}$ parallel to the $y$-axis. B: $ \qquad $ A translation of $5$ units in the positive $x$-direction. C: $ \qquad $ A reflection about $y$-axis. Find the equation of the resulting curve.[3] The diagram shows a sketch of the curve $y=\frac{1}{\mathrm{f}\left( x \right)}$. The curve cuts the axes at $\left( 2,0 \right)$ and $\left( 0,3 \right)$. It has a stationary point at $\left( -1,4 \right)$ and equations of asymptotes $x=3$ and $y=\frac{1}{2}$. Sketch the following curves and state the equations of the asymptotes, the coordinates of the turning points and of points where the curve crosses the axes. $y=\mathrm{f}\left( x \right)$.[3] $y=-\frac{1}{\mathrm{f}\left( x \right)}+4$.[3]

Accepted Answer

(a) $\dfrac{(x+7)^2}{4}+4y^2=1$ (b)(i) Asymptotes $x=2$ and $y=2$, minimum point $\left(-1,\dfrac14\right)$, axis crossings $(3,0)$ and $\left(0,\dfrac13\right)$ (b)(ii) Asymptotes $x=3$ and $y=\dfrac72$, minimum point and $x$-intercept $(-1,0)$, $y$-intercept $(0,1)$

2023 ACJC Promo Q3

2023 ACJC Promo Q3

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