9. A circle has centre \(C\) which lies on the \(x\)-axis, as shown in the diagram. The line \(y = x\) meets the circle at \(A\) and \(B\). The midpoint of \(A B\) is \(M\).
\includegraphics[max width=\textwidth, alt={}, center]{1e5d102a-955d-4968-8328-339f12665e01-20_776_730_280_214} The equation of the circle is \(x ^ { 2 } - 6 x + y ^ { 2 } + a = 0\), where \(a\) is a constant.

1. In this question you must show detailed reasoning. Find the \(x\)-coordinate of M and hence show that the area of triangle ABC is \(\frac { 3 } { 2 } \sqrt { 9 - 2 a }\).
2. 1. Find the value of \(a\) when the area of triangle \(A B C\) is zero.
   2. Give a geometrical interpretation of the case in part (b)(i).
3. Give a geometrical interpretation of the case where \(a = 5\).
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