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. 1,2
  2. 1,3
  3. 0,2
  4. $-2,2$

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 $k=2 .$

Asked in: MHT CET 2020 (14 Oct Shift 2)

Practice more Pair of Lines questions on Aicharya