The diagram shows part of the curve

\(y=\frac5{x-1}+2x,\)

and the straight lines \(x=4\) and \(2y=9x\).

(a) Find the coordinates of the stationary point on the curve

\(y=\frac5{x-1}+2x.\)

(b) Given that the curve and the line \(2y=9x\) intersect at the point \((2,9)\), find the area of the shaded region.