2015 HCI Promo Q12

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 \(C\).