Point P(x,y) is equidistant from the points A(5,1) and B(−1,5), means PA=PB or PA2=PB2(5−x)2+(1−y)2=(−1−x)2+(5−y)2(25+x2−10x)+(1−y2−2y)=(1+x2+2x+25+y2−10y)26+x2−10x+y2−2y=(26+x2+2x+y2−10y)12x=8y3x=2yHence proved.