9 A line has equation \(y = k x + 6\) and a curve has equation \(y = x ^ { 2 } + 3 x + 2 k\), where \(k\) is a constant.
- For the case where \(k = 2\), the line and the curve intersect at points \(A\) and \(B\). Find the distance \(A B\) and the coordinates of the mid-point of \(A B\).
- Find the two values of \(k\) for which the line is a tangent to the curve.