Edexcel C34 2015 June — Question 1

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2015
SessionJune
TopicImplicit equations and differentiation

  1. A curve has equation
$$4 x ^ { 2 } - y ^ { 2 } + 2 x y + 5 = 0$$ The points \(P\) and \(Q\) lie on the curve.
Given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2\) at \(P\) and at \(Q\),
  1. use implicit differentiation to show that \(y - 6 x = 0\) at \(P\) and at \(Q\).
  2. Hence find the coordinates of \(P\) and \(Q\).