Question

If the point P(x,y) is equidistant from the points A(a-b, a+b) and B(a+b, b-a) then prove
bx= ay.

Answer 1

P(x,y) = (a+b)+(a-b)/2 , (b-a)+(a+b)/2
P(x,y) =2a/2 , 2b/2
P(x,y) =a,b
Therefore, x=a and y=b.
To prove, bx=ay
b×a=a×b
ba=ab
Hence proved