Consider a family of curves given by \( y = a e^{x^2} \) , where a is a parameter.
Find the equation of the orthogonal trajectories for this family of curves.
1
\( y = -a e^{x^2} \)
2
\( y = a e^{x^3} \)
3
x= A \(e^{-y^2} \)
4
x= A \(e^{y^2} \)
Consider a family of curves given by \( y = a e^{x^2} \) , where a is a parameter.
Find the equation of the orthogonal trajectories for this family of curves.