2022 EJC J1 MYE Q8

A curve \(C\) has equation \(y=\frac{2{{x}^{2}}+5x-1}{x+3}\).

1. Using an algebraic method, determine the range of values that \(y\) can take.[3]
2. Sketch \(C\), labelling any turning points and equations of any asymptotes.[3]
3. On a separate diagram, sketch the graph of \({{\left( x-3 \right)}^{2}}+k{{y}^{2}}=k\) where \(1 < k\le 25\). Label all critical points clearly. Hence, determine all possible numbers of solutions to \({{\left( x-3 \right)}^{2}}+k{{\left( \frac{2{{x}^{2}}+5x-1}{x+3} \right)}^{2}}=k\).[3]