CAIE P3 2011 June — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionJune
TopicImplicit equations and differentiation

5 The curve with equation $$6 \mathrm { e } ^ { 2 x } + k \mathrm { e } ^ { y } + \mathrm { e } ^ { 2 y } = c$$ where \(k\) and \(c\) are constants, passes through the point \(P\) with coordinates \(( \ln 3 , \ln 2 )\).
  1. Show that \(58 + 2 k = c\).
  2. Given also that the gradient of the curve at \(P\) is - 6 , find the values of \(k\) and \(c\).