Question

If the point P(x,y) is equidistant from the point A(a+b,b-a) and B (a-b,a+b). Prove that bx=ay.​

Answer 1

.(a+b, b-a) & (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 - ax2 + (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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