Given: P(x,y) is equidistant from points A(3,4) and B(5,3) As we know that, distance between two points A and B is given by: |AB|=√(x2−x1)2+(y2−y1)2 ⇒|PA|=√(x−3)2+(y−4)2 .........(1) ⇒|PB|=√(x−5)2+(y−3)2 ........(2) ∵ |PA| = |PB| ⇒√(x−3)2+(y−4)2=√(x−5)2+(y−3)2 By squaring both the sides we get, ⇒(x−3)2+(y−4)2=(x−5)2+(y−3)2 ⇒(x2+9−6x)+(y2+16−8y)=(x2+25−10x)+(y2+9−6y) ⇒4x−16=2y−7 ⇒4x−2y=9 Hence, option C is the correct answer.