If the point p(x,y)is equidistant from the point a(1,5) and b(5,1)then

1.	If the point p(x,y)is equidistant from the point a(1,5) and b(5,1)then prove that x=y
Answer» Given , point P(x,y) is equidistant from points L(5,1) = (x1, y1) and M(-1,5)= (x2, y2).So, PL = PM{tex}\\Rightarrow PL^2=PM^2{/tex} [On squaring both sides]{tex}\\Rightarrow\\left(\\sqrt{{(x_\\;\\;-x_1)}^2+\\;(y\\;-y_1)^2}\\right)^2\\;=\\;\\left(\\sqrt{{(x\\;-x_2)}^2+\\;(y\\;\\;-y_2)^2}\\right)^2{/tex}{tex}\\Rightarrow (x-5)^2+(y-1)^2=(x+1)^2+(y-5)^2{/tex} [Using distance formula]⇒ x2 - 10x + 25 + y2 - 2y + 1 = x2 + 2x + 1 + y2 - 10y + 25⇒ - 10x - 2y + 26 = 2x - 10y + 26⇒ -10x - 2x = - 10y + 2y⇒ - 12 x = - 8y{tex}\\Rightarrow 3x=2y{/tex}

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