Edexcel C34 2019 January — Question 8

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2019
SessionJanuary
TopicParametric equations

8. A curve has parametric equations $$x = t ^ { 2 } - t , \quad y = \frac { 4 t } { 1 - t } \quad t \neq 1$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\), giving your answer as a simplified fraction.
  2. Find an equation for the tangent to the curve at the point \(P\) where \(t = - 1\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers. The tangent to the curve at \(P\) cuts the curve at the point \(Q\).
  3. Use algebra to find the coordinates of \(Q\).