2013 VJC P2 Q2

The curve \(C\) has equation \(y=\frac{a{{x}^{2}}+bx+c}{x-1}\), where \(a\), \(b\) and \(c\) are non-zero constants.

1. It is given that \(C\) passes through the point \(\left( 3,\ \frac{23}{2} \right)\)and has a minimum point at \(\left( 2,\ 10 \right)\).
   1. Find the values of \(a\), \(b\) and \(c\).[3]
   2. Sketch \(C\), giving the coordinates of any turning points, points of intersection with the axes and the equations of any asymptotes.[3]
   3. Find the set of values of \(\frac{m}{k}\), where \(m\) and \(k\) are positive constants, such that the curve with equation \(\frac{{{x}^{2}}}{{{k}^{2}}}-\frac{{{\left( y-1 \right)}^{2}}}{{{m}^{2}}}=1\) does not intersect \(C\).[2]
2. In the case when \(a=-1\) and \(b=-1\), find the set of values of \(c\), where \(c\ne 2\), such that \(C\) has no stationary point.[3]