CAIE P1 2011 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicDifferential equations

7 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 5 - \frac { 8 } { x ^ { 2 } }\). The line \(3 y + x = 17\) is the normal to the curve at the point \(P\) on the curve. Given that the \(x\)-coordinate of \(P\) is positive, find
  1. the coordinates of \(P\),
  2. the equation of the curve.