6 A curve is defined by the equation \(2 y + \mathrm { e } ^ { 2 x } y ^ { 2 } = x ^ { 2 } + C\), where \(C\) is a constant. The point \(P \left( 1 , \frac { 1 } { \mathrm { e } } \right)\) lies on the curve.
- Find the exact value of \(C\).
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- Verify that \(P \left( 1 , \frac { 1 } { \mathrm { e } } \right)\) is a stationary point on the curve.