11 The equation of a curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } - 30 x + 6 a\), where \(a\) is a positive constant. The curve has a stationary point at \(( a , - 15 )\).
- Find the value of \(a\).
- Determine the nature of this stationary point.
- Find the equation of the curve.
- Find the coordinates of any other stationary points on the curve.