CAIE P1 2024 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionNovember
TopicCircles

6 Circles \(C _ { 1 }\) and \(C _ { 2 }\) have equations $$x ^ { 2 } + y ^ { 2 } + 6 x - 10 y + 18 = 0 \text { and } ( x - 9 ) ^ { 2 } + ( y + 4 ) ^ { 2 } - 64 = 0$$ respectively.
  1. Find the distance between the centres of the circles.
    \(P\) and \(Q\) are points on \(C _ { 1 }\) and \(C _ { 2 }\) respectively. The distance between \(P\) and \(Q\) is denoted by \(d\).
  2. Find the greatest and least possible values of \(d\).