Question 7 - A-Level Maths

7 A circle with centre \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 4 x + 12 y + 15 = 0\).

Find:
1. the coordinates of \(C\);
2. the radius of the circle.
Explain why the circle lies entirely below the \(x\)-axis.
The point \(P\) with coordinates \(( 5 , k )\) lies outside the circle.
1. Show that \(P C ^ { 2 } = k ^ { 2 } + 12 k + 45\).
2. Hence show that \(k ^ { 2 } + 12 k + 20 > 0\).
3. Find the possible values of \(k\).