11 The coordinates of points \(A , B\) and \(C\) are \(A ( 5 , - 2 ) , B ( 10,3 )\) and \(C ( 2 p , p )\), where \(p\) is a constant.
- Given that \(A C\) and \(B C\) are equal in length, find the value of the fraction \(p\).
- It is now given instead that \(A C\) is perpendicular to \(B C\) and that \(p\) is an integer.
- Find the value of \(p\).
- Find the equation of the circle which passes through \(A , B\) and \(C\), giving your answer in the form \(x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0\), where \(a , b\) and \(c\) are constants.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.