OCR C4 2008 January — Question 9

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2008
SessionJanuary
TopicParametric equations

9 The parametric equations of a curve are \(x = t ^ { 3 } , y = t ^ { 2 }\).
  1. Show that the equation of the tangent at the point \(P\) where \(t = p\) is $$3 p y - 2 x = p ^ { 3 } .$$
  2. Given that this tangent passes through the point ( \(- 10,7\) ), find the coordinates of each of the three possible positions of \(P\).