CAIE P1 2005 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2005
SessionNovember
TopicStraight Lines & Coordinate Geometry

9 The equation of a curve is \(x y = 12\) and the equation of a line \(l\) is \(2 x + y = k\), where \(k\) is a constant.
  1. In the case where \(k = 11\), find the coordinates of the points of intersection of \(l\) and the curve.
  2. Find the set of values of \(k\) for which \(l\) does not intersect the curve.
  3. In the case where \(k = 10\), one of the points of intersection is \(P ( 2,6 )\). Find the angle, in degrees correct to 1 decimal place, between \(l\) and the tangent to the curve at \(P\).