8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f824c38-ae19-4889-a2e8-05a3707e9b27-3_496_716_1407_520}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the curve with equation \(y = 5 + x - x ^ { 2 }\) and the normal to the curve at the point \(P ( 1,5 )\).
- Find an equation for the normal to the curve at \(P\) in the form \(y = m x + c\).
- Find the coordinates of the point \(Q\), where the normal to the curve at \(P\) intersects the curve again.
- Show that the area of the shaded region bounded by the curve and the straight line \(P Q\) is \(\frac { 4 } { 3 }\).