Edexcel C2 2006 June — Question 7

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
TopicCircles

7. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{29c7baa1-6929-448a-a756-319ea75dffa7-08_611_682_296_641}
\end{figure} The line \(y = 3 x - 4\) is a tangent to the circle \(C\), touching \(C\) at the point \(P ( 2,2 )\), as shown in Figure 1. The point \(Q\) is the centre of \(C\).
  1. Find an equation of the straight line through \(P\) and \(Q\). Given that \(Q\) lies on the line \(y = 1\),
  2. show that the \(x\)-coordinate of \(Q\) is 5,
  3. find an equation for \(C\).