15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e878227b-d625-4ef2-ac49-a9dc05c5321a-40_883_824_212_568}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Diagram NOT drawn to scale
The points \(X\) and \(Y\) have coordinates \(( 0,3 )\) and \(( 6,11 )\) respectively. \(X Y\) is a chord of a circle \(C\) with centre \(Z\), as shown in Figure 3.
- Find the gradient of \(X Y\).
The point \(M\) is the midpoint of \(X Y\).
- Find an equation for the line which passes through \(Z\) and \(M\).
Given that the \(y\) coordinate of \(Z\) is 10 ,
- find the \(x\) coordinate of \(Z\),
- find the equation of the circle \(C\), giving your answer in the form
$$x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$$
where \(a\), \(b\) and \(c\) are constants.