The line \(y=12-2x\) is a tangent to two curves. Each curve has an equation of the form

\(y=k+6+kx-x^2,\)

where \(k\) is a constant.

(i) Find the two values of \(k\).

The line \(y=12-2x\) is a tangent to one curve at the point \(A\) and the other curve at the point \(B\).

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

(iii) Find the equation of the perpendicular bisector of \(AB\).