CAIE P2 2009 November — Question 8

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2009
SessionNovember
TopicImplicit equations and differentiation

8 The equation of a curve is \(y ^ { 2 } + 2 x y - x ^ { 2 } = 2\).
  1. Find the coordinates of the two points on the curve where \(x = 1\).
  2. Show by differentiation that at one of these points the tangent to the curve is parallel to the \(x\)-axis. Find the equation of the tangent to the curve at the other point, giving your answer in the form \(a x + b y + c = 0\).