If the point (x,y) be equidistant from the points `(a+b,b-a)` and `(a-b,a+b)`, then

Options

A. `ax=by`
B. `bx=ay`
C. `ax+by=0`
D. `bx+ay=0`

Answer

B

Explanation

Let `P(x,y),Q(a+b,b-a) and R(a-b,a+c)` be the given points. Then,
`PQ=QR" "` [Given]
`rArr sqrt([x-(a+b)]^(2)+[y-(b-a)]^(2))=sqrt([x-(a-b)]^(2)+[y-(a+b)]^(2))`
`rArr [x-(a+b)]^(2)+[y-(b-a)]^(2)=[x-(a-b)]^(2)+[y-(a+b)]^(2)`
`bx=ay`