If one of the lines represented by the equation `lambda y^(2)+(1-lambda^(2))xy-lambdax^(2)=0` is bisector of the angle between the lines `xy=0`, then, `lambda=`A. `1,-1`B. `2,-(1)/(2)`C. `1,2`D. `-1,-(1)/(2)`

If one of the lines represented by the equation `lambda y^(2)+(1-lambd

1.	If one of the lines represented by the equation `lambda y^(2)+(1-lambda^(2))xy-lambdax^(2)=0` is bisector of the angle between the lines `xy=0`, then, `lambda=`A. `1,-1`B. `2,-(1)/(2)`C. `1,2`D. `-1,-(1)/(2)`
Answer» Correct Answer - A 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`

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