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If the Point ( X,Y ) is Equidistant Form the Points ( A+B,B-a ) and (A-b ,A+B ) , Prove that Bx = Ay - Mathematics

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If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay

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Solution

As per the question, we have

`sqrt((x-a-b)^2 +(y-b+a)^2 ) = sqrt((x-a+b)^2 +(y-a-b)^2)`

`⇒(x-a-b)^2 +(y-b+a)^2 = (x-a+b)^2 +(y-a-b)^2`      (Squaring both sides) 

`⇒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)`

`⇒-x(a+b) - y (a-b) = -x(a-b) -y(a+b)`

`⇒-xa -xb -ay +by = -xa + bx -ya-by`

⇒ by=bx

Hence, . bx = ay 

Concept: Coordinate Geometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 17

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