If one of the lines given by $k x^{2}+x y-y^{2}=0$ bisects the angle between the co-ordinate axes, then…
If one of the lines given by $k x^{2}+x y-y^{2}=0$ bisects the angle between the co-ordinate axes, then values of $k$ are
1,2
1,3
0,2
$-2,2$
Solution
Given equation of lines is $k x^{2}+x y-y^{2}=0$
$\therefore \quad(-1) \mathrm{m}^{2}+\mathrm{m}+\mathrm{k}=0$ is auxillary equation
Since one line is angle bisector of coordinate axes, we write $m=\pm 1$.
When $m=1$, from auxillary equation, we get $k=0$.
When $m=-1$, from auxillary equation, we get $k=2 .$