9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f824c38-ae19-4889-a2e8-05a3707e9b27-4_757_855_246_482}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows the circle \(C\) with equation
$$x ^ { 2 } + y ^ { 2 } - 8 x - 10 y + 16 = 0$$
- Find the coordinates of the centre and the radius of \(C\).
\(C\) crosses the \(y\)-axis at the points \(P\) and \(Q\). - Find the coordinates of \(P\) and \(Q\).
The chord \(P Q\) subtends an angle of \(\theta\) at the centre of \(C\).
- Using the cosine rule, show that \(\cos \theta = \frac { 7 } { 25 }\).
- Find the area of the shaded minor segment bounded by \(C\) and the chord \(P Q\).
END