Edexcel P4 2022 January — Question 3

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJanuary
TopicImplicit equations and differentiation

3. The curve \(C\) has equation $$3 y ^ { 2 } - 11 x ^ { 2 } + 11 x y = 20 y - 36 x + 28$$
  1. Find, in simplest form, \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\). The point \(P ( 4 , k )\), where \(k\) is a constant, lies on \(C\).
    Given that \(k < 0\)
  2. find the value of the gradient of \(C\) at \(P\)