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

Chanchal Kumar Grade: 11

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

7 years ago

Answers : (2)

AJIT AskiitiansExpert-IITD

68 Points

Dear chanchal ,

i suggest simply apply hero's formula and use PA= PB or PA² = PB²

x-(a+b)² + y -(b-a)² = x-(a-b)² + y -(a+b)²

solving we get bx =ay. i don't think there is a need of doing angles equal or other method when this works perfectly.

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7 years ago

gOlU g3n|[0]uS

42 Points

										ans   if pts r equidistant then distance between them is equal
      AP² =  BP²  u can prove that        
    OR,
    if P is equidistant from A or B
   x=1(a+b) + 1(a-b)/2 =  a. ----1)

   y=1(a+b) + 1(b-a)/2 = b.  ----2)

THEN DIVIDE 1) and 2)...
  x/y=a/b =>bx=ya  HENCE PROVED..