CAIE P2 2005 November — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2005
SessionNovember
TopicImplicit equations and differentiation

4 The equation of a curve is \(x ^ { 3 } + y ^ { 3 } = 9 x y\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 3 y - x ^ { 2 } } { y ^ { 2 } - 3 x }\).
  2. Find the equation of the tangent to the curve at the point ( 2,4 ), giving your answer in the form \(a x + b y = c\).