Question

If one of the lines of the pair $a{x}^2+2hxy+b{y}^2=0$ bisects the angle between positive direction of the axes, then $a,b$ and $h$ satisfy the relation

• A. $a+b=2|h|$
• B. $a+b=-2h$
• C. $a-b=2|h|$
• D. $(a-b{)}^2=4h^2$

Answer 1

Answer: (B)

$a+b=-2h$

The angular bisectors of coordinate axes $(x=0,y=0)$ is $y=x$ and $y=-x.$

Bisector of positive direction of coordinate axes is $y=x.$

$\therefore y=x$, should satisfy $a{x}^2+2hxy+b{y}^2=0$

$\Rightarrow a+b+2h=0$

$\Rightarrow a+b=-2h$