Let P(x, y) be any point on the required locus. Given, A(1, 3), B(2, 1) and PA = PB
∴ PA2 = PB2
∴ (x – 1)2 + ( y – 3)2 = (x – 2)2 + (y – 1)2
∴ x2 – 2x + 1 + y2 – 6y + 9 = x2 – 4x + 4 + y2 – 2y + 1 -2x – 6y + 10 = -4x – 2y + 5
∴ 2x – 4y + 5 = 0
∴ The required equation of locus is 2x – 4y + 5 = 0.