11. The curve \(C\) has equation \(y = 2 x ^ { 3 } + k x ^ { 2 } + 5 x + 6\), where \(k\) is a constant.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
The point \(P\), where \(x = - 2\), lies on \(C\).
The tangent to \(C\) at the point \(P\) is parallel to the line with equation \(2 y - 17 x - 1 = 0\)
Find - the value of \(k\),
- the value of the \(y\) coordinate of \(P\),
- the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.