Edexcel C2 2014 January — Question 8

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2014
SessionJanuary
TopicCircles

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
  1. Write down the cartesian equation of \(C\). The points \(P ( - 3 , - 4 )\) and \(Q ( 3 , - 4 )\) lie on \(C\).
  2. Show that the tangent to \(C\) at the point \(Q\) has equation $$3 x - 4 y = 25$$
  3. 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 \(R\).
  4. 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}