Question

if a point (x,y) is equidistant from the point (a-b,a+b) and (b-a,a-b) the prove that (a-b)x+by=ab​​

Answer 1

Step-by-step explanation:

If the point p(x y) is equidistant from a(a+b b-a) and b(a-b a+b), bx = ay proved.

Answer 2

PA=PB

take square both side

PA^2=PB^2

now use distance

formula ,

{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 proved