1.41: Area bounded by line and hyperbola

The diagram shows the straight line and part of the curve . The straight line intersects the -axis at the point and intersects the curve at the point . The point lies on the curve. The point has coordinates . The line is parallel to the -axis.
(a)[3]
Find the coordinates of each of the points and .
(b)[6]
Find the area of the shaded region, giving your answer in the form , where and are positive integers.
