CAIE P1 2022 June — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicProduct & Quotient Rules

11 The point \(P\) lies on the line with equation \(y = m x + c\), where \(m\) and \(c\) are positive constants. A curve has equation \(y = - \frac { m } { x }\). There is a single point \(P\) on the curve such that the straight line is a tangent to the curve at \(P\).
  1. Find the coordinates of \(P\), giving the \(y\)-coordinate in terms of \(m\).
    The normal to the curve at \(P\) intersects the curve again at the point \(Q\).
  2. Find the coordinates of \(Q\) in terms of \(m\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.