If one of the lines of my^2+(1-m^2)xy-mx^2=0 is a bisector of the angle between the lines …

Question

If one of the lines of $my^2+(1-m^2)xy-mx^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ is:

Accepted Answer

Equation of bisectors of lines, $xy=0$ are $$y =  \pm x$$

$$\therefore$$ Put $$y =  \pm \,x$$ in the given equation

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

$$\therefore$$ $$m{x^2} + \left( {1 - {m^2}} \right){x^2} - m{x^2} = 0$$

$$ \Rightarrow 1 - {m^2} = 0 \Rightarrow m =  \pm 1$$

Solutions · 1