Let the moving point P be (x, y), then according to the problem, we must have;
PA + PB = 3 or (PA)2 = (3 - PB)2
(x - 1)2 + (y - 2)2 = 9 + {(x - 2)2 + (y - 1)2} - 6√(x - 2)2 + (y - 1)2} or
6√{(x - 2)2 + (y - 1)2 = 9 - 2x + 2y.
Squaring both sides and solving, we get;
32x2 + 32y2 - 8xy - 108x - 36y + 99 = 0.
It is required locus.