The equation of a curve is \(y = 3 + 4x - x^2\).

(i) Show that the equation of the normal to the curve at the point \((3, 6)\) is \(2y = x + 9\).

(ii) Given that the normal meets the coordinate axes at points \(A\) and \(B\), find the coordinates of the mid-point of \(AB\).

(iii) Find the coordinates of the point at which the normal meets the curve again.