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Find a relation between $x$ and $y$ such that $P(x, y)$ is equidistant from the points $A(3, 5)$ and $B(7, 1)$. Hence, write the coordinates of the points on $x$-axis and $y$-axis which are equidistant from points $A$ and $B$.
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$PA = PB \implies PA^2 = PB^2$
$(x-3)^2 + (y-5)^2 = (x-7)^2 + (y-1)^2$
$\implies x - y = 2$
$\therefore$ Required point on $x$-axis is $(2, 0)$
$\&$ required point on $y$-axis is $(0, -2)$
$(x-3)^2 + (y-5)^2 = (x-7)^2 + (y-1)^2$
$\implies x - y = 2$
$\therefore$ Required point on $x$-axis is $(2, 0)$
$\&$ required point on $y$-axis is $(0, -2)$