CAIE P1 2014 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionJune
TopicImplicit equations and differentiation

6 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 12 } { \sqrt { } ( 4 x + a ) }\), where \(a\) is a constant. The point \(P ( 2,14 )\) lies on the curve and the normal to the curve at \(P\) is \(3 y + x = 5\).
  1. Show that \(a = 8\).
  2. Find the equation of the curve.