[QUE/ME-02018] ME-PROBLEM

A particle of mass m moves on the inner surface of a cone of revolution, whose semi-vertical angle is \(\alpha\), under the action of arepulsive force \({m\mu/r^3}\) from the axis; the angular momentum of the particle about the axis being \(m\surd \mu \tan \alpha\); prove that its path is an arc of a hyperbola whose eccentricity is \(\sec \alpha\). . [Math. Tripos, 1897.]