The line joining the points \(A ( 4,5 )\) and \(B ( p , q )\) has mid-point \(M ( - 1,3 )\). Find \(p\) and \(q\).
\(A B\) is the diameter of a circle.
Find the radius of the circle.
Find the equation of the circle, giving your answer in the form \(x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0\).
Find an equation of the tangent to the circle at the point \(( 4,5 )\).