Question

if the point p(x,y) is equidistant from the points A(a+b,b-a) B(a-b,a+b). prove bx=ay

Answer 1

As we know...
√{(a+b−x)²+ (b−a−y)²} = √{(a−b−x)²+ (a+b−y)²}...(given that these are equidistant)...
Now by Squaring both sides we get
(a+b−x)²+ (b−a−y)²= (a−b−x)²+ (a+b−y)²
or (a+b−x)²− (a−b−x)²+ =(a+b−y)² − (b−a−y)²
[{(a+b−x)+(a−b−x)}×{(a+b−x)−(a−b−x)} =[{(a+b−y)+{(b−a−y)}×(a+b−y)−(b−a−y)}]
[{a+b−x+a−b−x}×{a+b−x−a+b+x} =[{a+b−y+b−a−y}×{a+b−y−b+a+y}]
[{2a−2x}×{2b}] =[{2b−2y}×{2a}]
4ab−4bx =4ab−4ay
−4bx =−4ay
bx=ay
Hope it helped u...!