4. The curve \(C\) has equation
$$3 y \mathrm { e } ^ { - 2 x } = 4 x ^ { 2 } + y ^ { 2 } + 2$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The point \(P\) on \(C\) has coordinates \(( 0,2 )\).
- Find the equation of the normal to \(C\) at \(P\) giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.
(3)
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