Edexcel P2 2018 Specimen — Question 7

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2018
SessionSpecimen
TopicCircles

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-19_739_871_260_532} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The circle with equation $$x ^ { 2 } + y ^ { 2 } - 20 x - 16 y + 139 = 0$$ had centre \(C\) and radius \(r\).
  1. Find the coordinates of \(C\).
  2. Show that \(r = 5\) The line with equation \(x = 13\) crosses the circle at the points \(P\) and \(Q\) as shown in Figure 1 .
  3. Find the \(y\) coordinate of \(P\) and the \(y\) coordinate of \(Q\). A tangent to the circle from \(O\) touches the circle at point \(X\).
  4. Find, in surd form, the length \(O X\).
    \includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-22_2673_1948_107_118}