Maths / Coordinate Geometry / Distance Formula

QUESTION
 

If the point (x, y) is equidistant from (a +b, b-a) and (a-b, a+b), show that bx =ay.

EXPLANATION
Explain TypeExplanation Content
Text

Let C =(x,y) A=(a + b, b-a) and B= (a-b, a+b)

large AC = sqrt{(x-(a+b))^2+(y-(b-a))^2}

large BC = sqrt{(x- (a-b))^2+(y-(a+b)^2}

As C is equidistant from A and B

AC= BC

large sqrt{(x-(a+b))^2+(y-(b-a))^2} =sqrt{(x- (a-b))^2+(y-(a+b)^2}

Squaring Both sides

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

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

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

large (x-a-b)+(x- a+b) (x-a-b)-(x- a+b)  

large =((y-a-b)+(y-b+a))((y-a-b)-(y-b+a))

large (2x-2a) (-2b) =(2y-2b)(-2a)  

large (-4xb+ 4ab) =(4ay+4ab)

large xb =ay

 

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