AQA C4 2006 June — Question 5

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2006
SessionJune
TopicImplicit equations and differentiation

5 A curve is defined by the equation $$y ^ { 2 } - x y + 3 x ^ { 2 } - 5 = 0$$
  1. Find the \(y\)-coordinates of the two points on the curve where \(x = 1\).
    1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y - 6 x } { 2 y - x }\).
    2. Find the gradient of the curve at each of the points where \(x = 1\).
    3. Show that, at the two stationary points on the curve, \(33 x ^ { 2 } - 5 = 0\).