CAIE P2 2017 November — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionNovember
TopicImplicit equations and differentiation

7 The equation of a curve is \(x ^ { 2 } + 4 x y + 2 y ^ { 2 } = 7\).
  1. Find the equation of the tangent to the curve at the point \(( - 1,3 )\). Give your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.
  2. Show that there is no point on the curve at which the gradient is \(\frac { 1 } { 2 }\).