CAIE P1 2013 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionJune
TopicQuadratic Functions

7 A curve has equation \(y = x ^ { 2 } - 4 x + 4\) and a line has equation \(y = m x\), where \(m\) is a constant.
  1. For the case where \(m = 1\), the curve and the line intersect at the points \(A\) and \(B\). Find the coordinates of the mid-point of \(A B\).
  2. Find the non-zero value of \(m\) for which the line is a tangent to the curve, and find the coordinates of the point where the tangent touches the curve.