CAIE P3 2023 June — Question 5 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionJune
Marks4
TopicImplicit equations and differentiation

5 The equation of a curve is \(x ^ { 2 } y - a y ^ { 2 } = 4 a ^ { 3 }\), where \(a\) is a non-zero constant.
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x y } { 2 a y - x ^ { 2 } }\).
  2. Hence find the coordinates of the points where the tangent to the curve is parallel to the \(y\)-axis. [4]