Question

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

Answer 1

Answer:

Since (x,y) is equidistant from A and B

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

x²+a²+b²-2ax+2ab-2bx+y²+b²+a²-2by-2ab+2ay = x²+a²+b²-2ax-2ab-2bx+y²+b²+a²-2by+2ab-2ay

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

4bx = 4ay

hence, bx = ay

Hence Proved

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