- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
A curve has equation
$$x ^ { 3 } + 2 x y + 3 y ^ { 2 } = 47$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\)
The point \(P ( - 2,5 )\) lies on the curve.
- Find the equation of the normal to the curve at \(P\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.