5 A circle with centre \(C ( 5 , - 3 )\) passes through the point \(A ( - 2,1 )\).
- Find the equation of the circle in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
- Given that \(A B\) is a diameter of the circle, find the coordinates of the point \(B\).
- Find an equation of the tangent to the circle at the point \(A\), giving your answer in the form \(p x + q y + r = 0\), where \(p , q\) and \(r\) are integers.
- The point \(T\) lies on the tangent to the circle at \(A\) such that \(A T = 4\). Find the length of \(C T\).