CAIE P1 2022 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicCircles

9 The equation of a circle is \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y - 26 = 0\).
  1. Find the coordinates of the centre of the circle and the radius. Hence find the coordinates of the lowest point on the circle.
  2. Find the set of values of the constant \(k\) for which the line with equation \(y = k x - 5\) intersects the circle at two distinct points.