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 \(C\).
- Find an equation of the straight line through \(P\) and \(Q\).
Given that \(Q\) lies on the line \(y = 1\),
- show that the \(x\)-coordinate of \(Q\) is 5,
- find an equation for \(C\).