2.60: Intersection of a curve and line, then shaded area

0606/23/M/J/17 — Question 11 · 10 marks

2.60 diagram
The diagram shows part of the curve y=5+10xy = 5 + \sqrt{10x} and the line 4y=5x+204y = 5x + 20. The line and curve intersect at the points P(0,5)P(0, 5) and QQ. The line QRQR is parallel to the yy-axis.
(i)
Find the coordinates of QQ.
[4]
(ii)
Find the area of the shaded region. You must show all your working.
[6]