The equation of a curve is \(y = 5 - \frac{8}{x}\).

(i) Show that the equation of the normal to the curve at the point \(P(2, 1)\) is \(2y + x = 4\).

This normal meets the curve again at the point \(Q\).

(ii) Find the coordinates of \(Q\).

(iii) Find the length of \(PQ\).