CAIE P3 2009 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2009
SessionNovember
TopicImplicit equations and differentiation

3 The equation of a curve is \(x ^ { 3 } - x ^ { 2 } y - y ^ { 3 } = 3\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
  2. Find the equation of the tangent to the curve at the point \(( 2,1 )\), giving your answer in the form \(a x + b y + c = 0\).