Question 5 - A-Level Maths

5 A circle with centre \(C\) has equation \(( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25\).

Write down:
1. the coordinates of \(C\);
2. the radius of the circle.
1. Verify that the point \(N ( 0 , - 2 )\) lies on the circle.
2. Sketch the circle.
3. Find an equation of the normal to the circle at the point \(N\).
The point \(P\) has coordinates (2, 6).
1. Find the distance \(P C\), leaving your answer in surd form.
2. Find the length of a tangent drawn from \(P\) to the circle.