11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b85872d4-00b2-499b-9765-f7559d3de66a-17_1000_956_264_500}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the circle \(C\) with centre \(Q\) and equation
$$x ^ { 2 } + y ^ { 2 } - 6 x + 2 y + 5 = 0$$
- Find
- the coordinates of \(Q\),
- the exact value of the radius of \(C\).
The tangents to \(C\) from the point \(T ( 8,4 )\) meet \(C\) at the points \(M\) and \(N\), as shown in Figure 4.
- Show that the obtuse angle \(M Q N\) is 2.498 radians to 3 decimal places.
The region \(R\), shown shaded in Figure 4, is bounded by the tangent \(T N\), the minor arc \(N M\), and the tangent \(M T\).
- Find the area of region \(R\).