8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e7043e7a-2c8f-425a-8471-f647828cc297-22_1015_1542_267_185}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a circle \(C\) with centre \(O\) and radius 5
- Write down the cartesian equation of \(C\).
The points \(P ( - 3 , - 4 )\) and \(Q ( 3 , - 4 )\) lie on \(C\).
- Show that the tangent to \(C\) at the point \(Q\) has equation
$$3 x - 4 y = 25$$
- Show that, to 3 decimal places, angle \(P O Q\) is 1.287 radians.
The tangent to \(C\) at \(P\) and the tangent to \(C\) at \(Q\) intersect on the \(y\)-axis at the point \(R\).
- Find the area of the shaded region \(P Q R\) shown in Figure 2.
\includegraphics[max width=\textwidth, alt={}, center]{e7043e7a-2c8f-425a-8471-f647828cc297-25_177_154_2576_1804}