CAIE P3 2022 June — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicImplicit equations and differentiation

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