A particle moves in the xy-plane acted on by a conservative force described by the potential energy U(x,y) = 2x2 + 8y2 +12xy + 12x + 18, where U is in units of J and x and y are in m.
(a) Calculate the magnitude and direction of the force on the particle at the point (x,y) = (2, - 1).
(b) At what point(s) is there no force?