For a synchronous machine with constant synchronous reactance Xs operating at a constant terminal voltage Vt and a constant excitation voltage Eaf, show that the locus of the tip of the armature-current phasor is a circle. On a phasor diagram with terminal voltage shown as the reference phasor, indicate the position of the center of this circle and its radius. Express the coordinates of the center and the radius of the circle in terms of Vt, Eaf and Xs.