Question

if if equidistant from the point (a+b,b-a)and (a-b,a+b) prove that BX = ay​

Answer 1

Answer

Let P(x,y), Q(a+b,b-a) and R(a-b,a+b) be the given points. Then,PQ=PR

⇒

{x−(a+b)}

2

+{y−(b−a)}

2

=

{x−(a−b)}

2

+{y−(a+b)}

2

⇒{x−(a+b)}

2

+{y−(b−a)}

2

={x−(a−b)}

2

+{y−(a+b)}

2

⇒x

2

−2x(a+b)+(a+b)

2

+y

2

−2y(b−a)+(b−a)

2

=x

2

+(a−b)

2

−2x(a−b)+y

2

−2y(a+b)+(a+b)

2

⇒−2x(a+b)−2y(b−a)=−2x(a−b)−2y(a+b)

⇒ax+bx+by−ay=ax−bx+ay+by

⇒2bx=2ay⇒bx=ay

Answer 2

Answer:

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