OCR C4 2006 January — Question 5

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
TopicParametric equations

5 A curve is given parametrically by the equations \(x = t ^ { 2 } , y = 2 t\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\), giving your answer in its simplest form.
  2. Show that the equation of the tangent to the curve at \(\left( p ^ { 2 } , 2 p \right)\) is $$p y = x + p ^ { 2 } .$$
  3. Find the coordinates of the point where the tangent at \(( 9,6 )\) meets the tangent at \(( 25 , - 10 )\).