7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{22ebc302-765c-4734-b312-b286ccb20be9-09_778_988_223_500}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The points \(A\) and \(B\) lie on a circle with centre \(P\), as shown in Figure 3.
The point \(A\) has coordinates \(( 1 , - 2 )\) and the mid-point \(M\) of \(A B\) has coordinates \(( 3,1 )\). The line \(l\) passes through the points \(M\) and \(P\).
- Find an equation for \(l\).
Given that the \(x\)-coordinate of \(P\) is 6 ,
- use your answer to part (a) to show that the \(y\)-coordinate of \(P\) is - 1 ,
- find an equation for the circle.