6 The surface \(C\) is given by the equation \(z = x ^ { 2 } + y ^ { 3 } + a x y\) for all real \(x\) and \(y\), where \(a\) is a non-zero real number.
- Show that \(C\) has two stationary points, one of which is at the origin, and give the coordinates of the second in terms of \(a\).
- Determine the nature of these stationary points of \(C\).
- Explain what can be said about the location and nature of the stationary point(s) of the surface given by the equation \(z = x ^ { 2 } + y ^ { 3 }\) for all real \(x\) and \(y\).