CAIE P3 2020 March — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionMarch
TopicImplicit equations and differentiation

7 The equation of a curve is \(x ^ { 3 } + 3 x y ^ { 2 } - y ^ { 3 } = 5\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x ^ { 2 } + y ^ { 2 } } { y ^ { 2 } - 2 x y }\).
  2. Find the coordinates of the points on the curve where the tangent is parallel to the \(y\)-axis.