Edexcel C2 2013 January — Question 5

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJanuary
TopicCircles

5. The circle \(C\) has equation $$x ^ { 2 } + y ^ { 2 } - 20 x - 24 y + 195 = 0$$ The centre of \(C\) is at the point \(M\).
  1. Find
    1. the coordinates of the point \(M\),
    2. the radius of the circle \(C\).
      \(N\) is the point with coordinates \(( 25,32 )\).
  2. Find the length of the line \(M N\). The tangent to \(C\) at a point \(P\) on the circle passes through point \(N\).
  3. Find the length of the line \(N P\).