The equation of a curve is \(y = 2x + \frac{12}{x}\) and the equation of a line is \(y + x = k\), where \(k\) is a constant.

In the case where \(k = 15\), the curve intersects the line at points \(A\) and \(B\).

(ii) Find the coordinates of \(A\) and \(B\).

(iii) Find the equation of the perpendicular bisector of the line joining \(A\) and \(B\).