OCR C4 2011 June — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2011
SessionJune
TopicParametric equations

8 A curve has parametric equations $$x = \frac { 1 } { t + 1 } , \quad y = t - 1 .$$ The line \(y = 3 x\) intersects the curve at two points.
  1. Show that the value of \(t\) at one of these points is - 2 and find the value of \(t\) at the other point.
  2. Find the equation of the normal to the curve at the point for which \(t = - 2\).
  3. Find the value of \(t\) at the point where this normal meets the curve again.
  4. Find a cartesian equation of the curve, giving your answer in the form \(y = \mathrm { f } ( x )\).