Question

If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines xy=0, then m=

• A. -2
• B. 1
• C. 2
• D. -1/2

Answer 1

The correct option is B 1

The bisectors of xy = 0 ie x = 0 and y = 0, we have are

$x+y=0$ and $x-y=0$

$\Rightarrow$ Now

$m{y}^2+(1-m^2)xy-m{x}^2=0$

$m{y}^2+1xy-m^{2}xy-m{x}^2=0$

$my(my+x)-mx(my+x)=0$

$\Rightarrow (y-mx)(my+x)=0$

on comparing there with x + y = 0 and x - y = 0 we have

m = 1