Question

Find a relation between $x$ and $y$ such that the point $(x,y)$ is equidistant from the points $(7,1)$ and $(3,5)$.

Answer 1

Point $(x,y)$ is equidistant from $(7,1)$ and $(3,5)$

$\sqrt{(x-7{)}^2+(y-1{)}^2}=\sqrt{(x-3{)}^2+(y-5{)}^2}$

$x^2+49-14x+y^2+1-2y=x^2+9-6x+y^2+25-10y$

$14x-6x-10y+2y+34-50=0$

$8x-8y-16=0$

$x-y-z=0$

is the relation between $x$ & $y.$