Given, let P(x,y) be any point. A = (1, 2) and B = (-2,3). A point P (x, y) moves such that its distances from A = (1, 2) and B = (-2, 3) are equal. ⇒ PA = PB ⇒(PA)2=(PB)2 By Distance formula, (x−1)2+(y−2)2=(x+2)2+(y−3)2 ⇒x2−2x+1+y2−4y+4=x2+4x+4+y2−6y+9 ⇒6x−2y+8=0 ⇒3x−y+4=0 which represent the equation of line. Hence, the locus of P is a straight line