Question

If the point $(x,y)$ be equidistance from the point $(a+b,b-a)$ and $(a-b,a+b)$ , prove that $bx=ay$.

Answer 1

$(x,y)$ is equidistant from $A(a+b,b-a)$ & $B(a-b,a+b)$

=> $x,y$ cuts AB in equal parts.

=>$(x,y)=(\frac{a+b+a-b}{2},\frac{b-a+a+b}{2})(x,y)=(a,b)=>x=a\&b=y$

so, $xb=ay$ (multiplying them both)