If the point `P(p,q)` is equidistant from the points `A(a+b,b-a)and B(a-b,a+b),` then

Options

A. x-y=0
B. ax + by =0
C. bx +ay =0
D. x+y=0

Answer

A

Explanation

Let coordinates of point P be (x,y)
Given , PA = PB ` Rightarrow (PA)^(2) = (PB)^(2)`
` Rightarrow {x - (a+b)}^(2) + {y -(a-b)}^(2)`
` = {x-(a-b)}^(2) + {y-(a+b)}^(2)`
` Rightarrow x^(2) + (a+b)^(2) -2x (a+b)+y^(2) + (a-b)^(2) -2y(a-b)`
` =x^(2) + (a-b)^(2) -2x (a-b)+y^(2) + (a+b)^(2) -2y(a+b)`
` Rightarrow 2x(-a-b+a-b) +2y (-a+b+a+b) = 0`
`Rightarrow -2bx + 2by =0`
-x +y =0
x-y=0