10 Points \(A\) and \(B\) have coordinates \(( 4,3 )\) and \(( 8 , - 5 )\) respectively. A circle with radius 10 passes through the points \(A\) and \(B\).
- Show that the centre of the circle lies on the line \(y = \frac { 1 } { 2 } x - 4\).
\includegraphics[max width=\textwidth, alt={}, center]{49e137bf-42cc-41af-b5d9-85301d4699b8-14_2715_35_109_2010} - Find the two possible equations of the circle.