If the distances of P(x,y) from A(5,1) and B(-1,5) are equal, then prove that 3x=2y.

If the distances of P(x,y) from A(5,1) and B(-1,5) are equal, then pro

1.	If the distances of P(x,y) from A(5,1) and B(-1,5) are equal, then prove that 3x=2y.
Answer» Considering AZ = ZB, that means {tex}A Z^{2}=Z B^{2}{/tex}{tex}(x-5)^{2}+(y-1)^{2}=(x+1)^{2}+(y-5)^{2}{/tex}Squaring both the sides we get the factors and then simplifying them we get:{tex}x^{2}+25-10 x+y^{2}+1-2 y=x^{2}+1+2 x+y^{2}+25-10 y{/tex}12x = 8y3x = 2y Hence proved