AQA C4 2008 June — Question 2

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
TopicParametric equations

2 A curve is defined, for \(t \neq 0\), by the parametric equations $$x = 4 t + 3 , \quad y = \frac { 1 } { 2 t } - 1$$ At the point \(P\) on the curve, \(t = \frac { 1 } { 2 }\).
  1. Find the gradient of the curve at the point \(P\).
  2. Find an equation of the normal to the curve at the point \(P\).
  3. Find a cartesian equation of the curve.