2024 TJC P2 Q1

A curve \({C}\) has equation \({y = \frac{3 - x}{x - 1}}\).

1. Sketch \({C}\), stating the equations of the asymptotes.[2]
2. Find the exact volume of the solid generated when the region bounded by \({C}\), the \({x}\)-axis and the line \({x=9}\) is rotated through \({2\pi}\) radians about the \({x}\)-axis. Leave your answer in the form \({\pi (a + b \ln 2)}\), where \({a}\) and \({b}\) are constants to be determined.[5]