Problem 1.132

In a certain two-dimensional field of force the potential energy of a particle has the form $U=\alpha x^{2}+\beta y^{2}$, where $\alpha$ and $\beta$ are positive constants whose magnitudes are different. Find out: (a) whether this field is central; (b) what is the shape of the equipotential surfaces and also of the surfaces for which the magnitude of the vector of force $F=$ const.