9.
\includegraphics[max width=\textwidth, alt={}, center]{33f9663f-26bb-445e-af6e-ca5ca927f7dd-3_638_757_1064_493}
The diagram 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 \(\frac { 4 } { 3 }\).