CAIE P3 2022 June — Question 8

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

8 The equation of a curve is \(x ^ { 3 } + y ^ { 3 } + 2 x y + 8 = 0\).
  1. Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
    The tangent to the curve at the point where \(x = 0\) and the tangent at the point where \(y = 0\) intersect at the acute angle \(\alpha\).
  2. Find the exact value of \(\tan \alpha\).