Question

if the point p(x,y) is equidistant from the points Q(a+b,b-a) and R(a-b,a+b), then prove that bx=ay

Answer 1

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Answer 2

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Distance between the points (x,y) and (a+b, b-a) and (a-b, a+b) is equal

=> √{[x - (a+b)]² + [y - (b-a)]²} = √{x - (a-b)]² + [y - (a+b)]²}

=> x² + (a+b)² - 2x(a+b) + y² + (b-a)² - 2y(b-a) = x² + (a-b)² - 2x(a-b) + y² + (a+b)² - 2y(a+b)

=> -2ax - 2bx - 2by + 2ay = -2ax + 2bx - 2ay - 2by

=> ay - bx = bx - ay

=> 2ay = 2bx

=> bx = ay




HENCE PROVED!!!


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