7.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{beec3800-227a-45a1-87b8-0ea96e0e6270-4_661_746_283_721}
\end{figure}
The points \(A\) and \(B\) have coordinates \(( 2 , - 3 )\) and \(( 8,5 )\) respectively, and \(A B\) is a chord of a circle with centre \(C\), as shown in Fig. 1.
- Find the gradient of \(A B\).
The point \(M\) is the mid-point of \(A B\).
- Find an equation for the line through \(C\) and \(M\).
(5)
Given that the \(x\)-coordinate of \(C\) is 4 , - find the \(y\)-coordinate of \(C\),
(2) - show that the radius of the circle is \(\frac { 5 \sqrt { } 17 } { 4 }\).
(4)