OCR C4 2009 June — Question 5

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
TopicParametric equations

5 A curve has parametric equations $$x = 2 t + t ^ { 2 } , \quad y = 2 t ^ { 2 } + t ^ { 3 }$$
  1. Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\) and find the gradient of the curve at the point \(( 3 , - 9 )\).
  2. By considering \(\frac { y } { x }\), find a cartesian equation of the curve, giving your answer in a form not involving fractions.