3 A circle has equation \(x ^ { 2 } + y ^ { 2 } - 12 x - 6 y + 20 = 0\).
- By completing the square, express the equation in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }$$
- Write down:
- the coordinates of the centre of the circle;
- the radius of the circle.
- The line with equation \(y = x + 4\) intersects the circle at the points \(P\) and \(Q\).
- Show that the \(x\)-coordinates of \(P\) and \(Q\) satisfy the equation
$$x ^ { 2 } - 5 x + 6 = 0$$
- Find the coordinates of \(P\) and \(Q\).