[QUE/CM-05010]

A particle moves in a central potential $$ V(r) = -{\alpha \over r^2} $$       and has energy $E$, angular momentum $L$. Show that the orbit of the particle is given by $$ {1\over r} = \sqrt{2mE\over L^2 -2m\alpha } \cos ( \lambda (\phi + \delta))$$  where $\lambda ^2 =1- {2m\alpha \over L^2}$