The ellipse ${{C}_{1}}$ with the equation \(\frac{{{x}^{2}}}{{{6}^{2}}}+\frac{{{y}^{2}}}{{{3}^{2}}

Question

The ellipse ${{C}_{1}}$ with the equation $\frac{{{x}^{2}}}{{{6}^{2}}}+\frac{{{y}^{2}}}{{{3}^{2}}}=1$ is transformed by a stretch with scale factor $k$ parallel to the $x$-axis, followed by a translation of $m$ units in the positive $x$-direction, followed by a translation of $n$ units in the negative $y$-direction, to form ${{C}_{2}}$. Find the equation of ${{C}_{2}}$ in terms of $k$, $m$ and $n$.[3] Given that ${{C}_{2}}$ is a circle centred at $\left( 4,-7 \right)$, find the values of $k$, $m$ and $n$.[2]

Accepted Answer

(i) ${C_2 : \frac{(x-m)^2}{(6k)^2} + \frac{(y+n)^2}{3^2} = 1}$ (ii) ${k = \frac{1}{2}\;, m = 4\;, n = 7}$

2015 SAJC P1 Q5

2015 SAJC P1 Q5

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