Find curve equation from dy/dx

A question is this type if and only if it gives dy/dx as a function and asks to find the equation of the curve using integration and boundary conditions.

1 questions · Moderate -0.3

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CAIE P1 2014 June Q6
7 marks Moderate -0.3
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.