OCR C4 2011 January — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2011
SessionJanuary
TopicImplicit equations and differentiation

8 The points \(P\) and \(Q\) lie on the curve with equation $$2 x ^ { 2 } - 5 x y + y ^ { 2 } + 9 = 0$$ The tangents to the curve at \(P\) and \(Q\) are parallel, each having gradient \(\frac { 3 } { 8 }\).
  1. Show that the \(x\) - and \(y\)-coordinates of \(P\) and \(Q\) are such that \(x = 2 y\).
  2. Hence find the coordinates of \(P\) and \(Q\).