6. 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 a circle,
- find the coordinates of the centre of the circle,
- show that the equation of the circle can be written in the form
$$x ^ { 2 } + y ^ { 2 } - 4 x - 6 y = k$$
where \(k\) is an integer to be found.