8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2bacec90-3b67-4307-9608-246ecdb6b5e2-28_664_844_255_612}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve \(C\) with parametric equations
$$x = t + \frac { 1 } { t } \quad y = t - \frac { 1 } { t } \quad t > 0.7$$
The curve \(C\) intersects the \(x\)-axis at the point \(Q\).
- Find the \(x\) coordinate of \(Q\).
The line \(l\) is the normal to \(C\) at the point \(P\) as shown in Figure 2.
Given that \(t = 2\) at \(P\) - write down the coordinates of \(P\)
- Using calculus, show that an equation of \(l\) is
$$3 x + 5 y = 15$$
The region, \(R\), shown shaded in Figure 2 is bounded by the curve \(C\), the line \(l\) and the \(x\)-axis.
- Using algebraic integration, find the exact volume of the solid of revolution formed when the region \(R\) is rotated through \(2 \pi\) radians about the \(x\)-axis.