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

Options

A. `1,-1`
B. `2,-(1)/(2)`
C. `1,2`
D. `-1,-(1)/(2)`

Answer

A

Explanation

We have,
`xy=0 rArr x = 0 or y =0 `
Thus, xy = 0 represent the coordinate axes.
The equation of the angle bisectors between the coordinate axes are y = x and `y=-x`.
It is given that one of the lines represented by the equaiton
`lambday^(2)+(1-lambda^(2))xy- lambda x^(2)=0" ....(i)"`
is `y=x or , y=-x`
`therefore" "lambda+1-lambda^(2)-lambda=0" "["Putting y = x on (i)"]`
or, `lambda-(1-lambda^(2))-lambda=0" "["Putting "y=-x " in (i)"]`
`rArr" "1-lambda^(2)=0 rArr lambda = pm 1`