Question

If $M(x,y)$ is equidistant from $A(a+b,b-a)$ and $B(a-b,a+b)$, then

• A. $bx+ay=0$
• B. $bx-ay=0$
• C. $ax+by=0$
• D. $ax-by=0$

Answer 1

Answer: (B)

$bx-ay=0$

Distance between two points $=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Given, Distance between the points $(x,y);(a+b,b-a)=$ Distance between $(x,y);(a-b,a+b)$

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

$=>{(a+b-x)}^2+{(b-a-y)}^2={(a-b-x)}^2+{(a+b-y)}^2$

$=>{(a+b)}^2+x^2-2(a+b)x+{(b-a)}^2+y^2-2(b-a)y={(a-b)}^2+x^2-2(a-b)x+{(a+b)}^2+y^2-2(a+b)y$

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

$=>4bx=4ay$

$=>bx-ay=0$