CAIE P2 2008 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2008
SessionJune
TopicImplicit equations and differentiation

7 The equation of a curve is $$x ^ { 2 } + y ^ { 2 } - 4 x y + 3 = 0$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 y - x } { y - 2 x }\).
  2. Find the coordinates of each of the points on the curve where the tangent is parallel to the \(x\)-axis.