Question

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

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

Answer 1

The correct option is B $a+b=-2h$

Equation of angle bisector of first quadrant is $y-x=0$

So, it is one of the lines of the given pair of straight lines

So, $x^2(2h+a+b)=0$

$\Rightarrow -2h=a+b$