Edexcel P2 2021 October — Question 6

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2021
SessionOctober
TopicCircles

6. (i) The circle \(C _ { 1 }\) has equation $$x ^ { 2 } + y ^ { 2 } + 10 x - 12 y = k \quad \text { where } k \text { is a constant }$$
  1. Find the coordinates of the centre of \(C _ { 1 }\)
  2. State the possible range in values for \(k\).
    (ii) The point \(P ( p , 0 )\), the point \(Q ( - 2,10 )\) and the point \(R ( 8 , - 14 )\) lie on a different circle, \(C _ { 2 }\) Given that
    • \(p\) is a positive constant
    • \(Q R\) is a diameter of \(C _ { 2 }\)
      find the exact value of \(p\).