1.41: Area bounded by line and hyperbola

0606/12/M/J/20 — Question 6 · 9 marks

1.41 diagram
The diagram shows the straight line 2x+y=52x + y = -5 and part of the curve xy+3=0xy + 3 = 0. The straight line intersects the xx-axis at the point AA and intersects the curve at the point BB. The point CC lies on the curve. The point DD has coordinates (1,0)(1, 0). The line CDCD is parallel to the yy-axis.
(a)
Find the coordinates of each of the points AA and BB.
[3]
(b)
Find the area of the shaded region, giving your answer in the form p+lnqp + \ln q, where pp and qq are positive integers.
[6]