CAIE P3 2016 June — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionJune
TopicImplicit equations and differentiation

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