AQA Paper 3 2019 June — Question 9

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2019
SessionJune
TopicImplicit equations and differentiation

9 A curve has equation $$x ^ { 2 } y ^ { 2 } + x y ^ { 4 } = 12$$ 9
  1. Prove that the curve does not intersect the coordinate axes.
    9
    1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 2 x y + y ^ { 3 } } { 2 x ^ { 2 } + 4 x y ^ { 2 } }\)
      9
  2. (ii) Prove that the curve has no stationary points.
    9
  3. (iii) In the case when \(x > 0\), find the equation of the tangent to the curve when \(y = 1\)