10 A straight line has equation \(y = - 2 x + k\), where \(k\) is a constant, and a curve has equation \(y = \frac { 2 } { x - 3 }\).
- Show that the \(x\)-coordinates of any points of intersection of the line and curve are given by the equation \(2 x ^ { 2 } - ( 6 + k ) x + ( 2 + 3 k ) = 0\).
- Find the two values of \(k\) for which the line is a tangent to the curve.
The two tangents, given by the values of \(k\) found in part (ii), touch the curve at points \(A\) and \(B\).
- Find the coordinates of \(A\) and \(B\) and the equation of the line \(A B\).