8. The points \(P , Q\) and \(R\) have coordinates \(( - 5,2 ) , ( - 3,8 )\) and \(( 9,4 )\) respectively.
- Show that \(\angle P Q R = 90 ^ { \circ }\).
Given that \(P , Q\) and \(R\) all lie on circle \(C\),
- find the coordinates of the centre of \(C\),
- show that the equation of \(C\) can be written in the form
$$x ^ { 2 } + y ^ { 2 } + a x + b y = k$$
where \(a , b\) and \(k\) are integers to be found.
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