CAIE P1 2010 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionNovember
TopicInequalities

6 A curve has equation \(y = k x ^ { 2 } + 1\) and a line has equation \(y = k x\), where \(k\) is a non-zero constant.
  1. Find the set of values of \(k\) for which the curve and the line have no common points.
  2. State the value of \(k\) for which the line is a tangent to the curve and, for this case, find the coordinates of the point where the line touches the curve.