8 A circle with centre \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 6 x - 16 y + 48 = 0\).
- Find the coordinates of C .
A line has equation \(\mathrm { y } = \mathrm { x } - 2\) and intersects the circle at the points A and B . The midpoints of AC and BC are \(\mathrm { A } ^ { \prime }\) and \(\mathrm { B } ^ { \prime }\) respectively.
- Determine the exact distance \(\mathrm { A } ^ { \prime } \mathrm { B } ^ { \prime }\).