6. A curve has equation
$$4 y ^ { 2 } + 3 x = 6 y \mathrm { e } ^ { - 2 x }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The curve crosses the \(y\)-axis at the origin and at the point \(P\).
- Find the equation of the normal to the curve at \(P\), writing your answer in the form \(y = m x + c\) where \(m\) and \(c\) are constants to be found.