2021 VJC Promo Q4

The diagram below shows the graph of \(y=\mathrm{f}\left( -x+1 \right)\) which has a minimum point at \(\left( -2,4 \right)\) and has lines \(y=\frac{x}{2}+4\) and \(y=-\frac{x}{2}+2\) as asymptotes.

1. The diagram above shows a part of the curve with equation \(\frac{{{\left( y+a \right)}^{2}}}{m}-\frac{{{\left( x+b \right)}^{2}}}{k}=1\). Find the values of \(a\), \(b\) and \(k\).[4]
2. Sketch the graph of \(y=\mathrm{f}\left( x \right)\).[2]