OCR C4 2008 June — Question 3

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

3 The equation of a curve is \(x ^ { 2 } y - x y ^ { 2 } = 2\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } - 2 x y } { x ^ { 2 } - 2 x y }\).
  2. (a) Show that, if \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\), then \(y = 2 x\).
    (b) Hence find the coordinates of the point on the curve where the tangent is parallel to the \(x\)-axis.