5 A circle with centre \(C ( - 5,6 )\) touches the \(y\)-axis, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{66813123-3876-4484-aad1-4bfc09bb1508-6_444_698_372_680}
- Find the equation of the circle in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }$$
- Verify that the point \(P ( - 2,2 )\) lies on the circle.
- Find an equation of the normal to the circle at the point \(P\).
- The mid-point of \(P C\) is \(M\). Determine whether the point \(P\) is closer to the point \(M\) or to the origin \(O\).