CAIE P1 2021 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionNovember
TopicCircles

9 The line \(y = 2 x + 5\) intersects the circle with equation \(x ^ { 2 } + y ^ { 2 } = 20\) at \(A\) and \(B\).
  1. Find the coordinates of \(A\) and \(B\) in surd form and hence find the exact length of the chord \(A B\).
    A straight line through the point \(( 10,0 )\) with gradient \(m\) is a tangent to the circle.
  2. Find the two possible values of \(m\).