CAIE P2 2006 June — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2006
SessionJune
TopicImplicit equations and differentiation

5 The equation of a curve is \(3 x ^ { 2 } + 2 x y + y ^ { 2 } = 6\). It is given that there are two points on the curve where the tangent is parallel to the \(x\)-axis.
  1. Show by differentiation that, at these points, \(y = - 3 x\).
  2. Hence find the coordinates of the two points.