[QUE/CM-02027]

A particle moves in two dimensions in potential given by \[ V(x,y)= \frac{\lambda}{r} \] where \(r=\sqrt{x^2+y^2}\). Set up the Lagrangian for the system in parabolic coordinates \(u,v\) defined by \[ x= u^2-v^2, \quad y=2u v.\]