5 A circle with centre \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = 11\).
- By completing the square, express this equation in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }$$
- Write down:
- the coordinates of \(C\);
- the radius of the circle.
- The point \(O\) has coordinates \(( 0,0 )\).
- Find the length of CO .
- Hence determine whether the point \(O\) lies inside or outside the circle, giving a reason for your answer.