If the points (x,y) are equidistant from the points (a+b,b-a) and (a-b,a+b),prove that bx = ay.

Explanation

Given that `bar(AP) = bar(BP)`
`therefore sqrt((x-a-b)^2 + (y-b+a)^2)` ,
= `sqrt((x-a+b)^2 + (y-b+a)^2)`
or, `x^2 + a^2 + b^2 -2ax + 2ab - abx + y^2 +b^2 + a^2 -2by-2ab-2ay`
= `x^2 + a^2 + b^2 -2ax-2ab-2by`
or, 4bx = 4ay or, bx = ay .