9. The points \(A\) and \(B\) have coordinates \(( - 2,11 )\) and \(( 8,1 )\) respectively.
Given that \(A B\) is a diameter of the circle \(C\),
- show that the centre of \(C\) has coordinates \(( 3,6 )\),
- find an equation for \(C\).
- Verify that the point \(( 10,7 )\) lies on \(C\).
- Find an equation of the tangent to \(C\) at the point (10, 7), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants.