The curve $C$ has equation $4{{x}^{2}}+{{y}^{2}}+8mx-4y+4=0$, where $m\in \mathbb{R}$ , $m0$. Show

Question

The curve $C$ has equation $4{{x}^{2}}+{{y}^{2}}+8mx-4y+4=0$, where $m\in \mathbb{R}$ , $m>0$. Show that $C$can be expressed in the form ${{\left( \frac{x+a}{b} \right)}^{2}}+{{\left( \frac{y+c}{d} \right)}^{2}}=1$, where $a$ , $b$ , $c$ and $d$ are constants to be determined in terms of $m$ . Hence describe a sequence of transformations, in terms of $m$, which transforms the graph of ${{x}^{2}}+{{\left( y-\frac{1}{m} \right)}^{2}}=1$ to $C$. [6]

Accepted Answer

$C: \left(\dfrac{x+m}{m}\right)^2+\left(\dfrac{y-2}{2m}\right)^2=1$, with $a=m$, $b=m$, $c=-2$, $d=2m$ One sequence: scale parallel to the $x$-axis by $m$, translate $m$ units left, then scale parallel to the $y$-axis by $2m$

2015 HCI Promo Q2

2015 HCI Promo Q2

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