\\\\(\ extbf{Step 1: Find the relation between x and y}.\\\\) \\\\(\ ext{Let P(x, y) be equidistant from the points A(7,1) and B(3,5).}\\\\) \\\\(\ ext{So, AP = BP}\\\\) \\\\(\ ext{Squaring on both sides, we get}\\\\) \\\\( \\Rightarrow (AP)^2=(BP)^2\\\\) \\\\(\ ext{Using, distance formula, }\\\\) \\\\(\ ext{Distance between}\\ (x_1,y_1)\\ \ ext{and} \\ (x_2,y_2)= \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.....(1)\\\\) \\\\(\ ext{Now,}\\\\) \\\\( \\Rightarrow (AP)^2=(BP)^2\\\\) \\\\(\\Rightarrow (x-7)^2+(y-1)^2=(x-3)^2+(y-5)^2\\\\) \\\\(\ extbf{[Using eq(1)]}\\\\) \\\\(\\Rightarrow x^2+49-14x+y^2+1-2y=x^2+9-6x+y^2+25-10y\\\\) \\\\(\\Rightarrow -14x+50-2y=-6x+34-10y\\\\) \\\\(\\Rightarrow -7x+25-y=-3x+17-5y\\\\) \\\\(\\Rightarrow -4x+8+4y=0\\\\) \\\\(\\Rightarrow 4x-4y=8\\\\) \\\\(\\Rightarrow 4(x-y)=8\\\\) \\\\(\\Rightarrow x-y=2\\\\)\\\\(\ extbf{Hence, this is the required relation between x and y . }\\\\)