The surface of a paraboloid of revolution is defined by \(z=a\left(x^{2}+y^{2}ight)\) where \(a\) is a constant. Find the differential equation for a geodesic originating at a point \((x, y)=\) \(\left(x_{0}, 0ight)\) with slope \((d y / d x)_{0}=0\). Does the geodesic return to the same point?