CAIE P1 2012 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicStraight Lines & Coordinate Geometry

10 The equation of a line is \(2 y + x = k\), where \(k\) is a constant, and the equation of a curve is \(x y = 6\).
  1. In the case where \(k = 8\), the line intersects the curve at the points \(A\) and \(B\). Find the equation of the perpendicular bisector of the line \(A B\).
  2. Find the set of values of \(k\) for which the line \(2 y + x = k\) intersects the curve \(x y = 6\) at two distinct points.