If the point `(x , y)` is equidistant from the points `(a+b , b-a)` and `(a-b , a+b)` , prove that `b x=a y`

Explanation

To prove that \( b x = a y \) given that the point \( (x, y) \) is equidistant from the points \( (a+b, b-a) \) and \( (a-b, a+b) \), we can follow these steps:

### Step 1: Set up the distance equations

The distance from point \( (x, y) \) to point \( (a+b, b-a) \) is given by the distance formula:

\[
d_1 = \sqrt{(x - (a+b))^2 + (y - (b-a))^2}
...