Q:

If the points (x,y) be equidistant from the points A(a+b,b-a) and B(a-b,a+b), prove that bx-ay=0​

Accepted Solution

A:
Solution:-It is given that the points (x,y) be equidistant from the points A(a+b,b-a) and B(a-b,a+b).PA=PBTake square both side,PA^2=PB^2Now use distanceformula ,{x-(a+b)}^2+{y-(b-a)}^2={x-(a-b)}^2+{y-(a+b)}^2=>x^2+(a+b)^2-2x(a+b)+y^2+(b-a)^2-2y(b-a)y=x^2+(a-b)^2-2x(a-b)+y^2+(a+b)^2-2y(a+b)=>2x(a-b)-2x(a+b)=2y(b-a)-2y(a+b)=>2x{a-b-a-b}=2y{b-a-a-b}=>2x(-2b)=2y(-2a)=>bx=ay Hence, it is proved.