Edexcel C4 2008 June — Question 4

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
TopicImplicit equations and differentiation

4. A curve has equation \(3 x ^ { 2 } - y ^ { 2 } + x y = 4\). The points \(P\) and \(Q\) lie on the curve. The gradient of the tangent to the curve is \(\frac { 8 } { 3 }\) at \(P\) and at \(Q\).
  1. Use implicit differentiation to show that \(y - 2 x = 0\) at \(P\) and at \(Q\).
  2. Find the coordinates of \(P\) and \(Q\).