CAIE P2 2019 November — Question 7 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2019
SessionNovember
Marks5
TopicImplicit equations and differentiation

7 The equation of a curve is \(x ^ { 2 } - 4 x y - 2 y ^ { 2 } = 1\).
  1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and show that the gradient of the curve at the point \(( - 1,2 )\) is \(- \frac { 5 } { 2 }\). [5]
  2. Show that the curve has no stationary points.
  3. Find the \(x\)-coordinate of each of the points on the curve at which the tangent is parallel to the \(y\)-axis.
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