The coordinates of two points \(A\) and \(B\) are \(( - 7,3 )\) and \(( 5,11 )\) respectively.
Show that the equation of the perpendicular bisector of \(A B\) is \(3 x + 2 y = 11\).
A circle passes through \(A\) and \(B\) and its centre lies on the line \(12 x - 5 y = 70\).
Find an equation of the circle.