6. The circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } - 6 x + 4 y = 12$$
- Find the centre and the radius of \(C\).
The point \(P ( - 1,1 )\) and the point \(Q ( 7 , - 5 )\) both lie on \(C\).
- Show that \(P Q\) is a diameter of \(C\).
The point \(R\) lies on the positive \(y\)-axis and the angle \(P R Q = 90 ^ { \circ }\).
- Find the coordinates of \(R\).