The value of `lambda` for which the lines joining the point of intersection of curves `C_(1)` and `C_(2)` to the origin are equally inclined to the axis of x. `C_(1):lambdax^(2)+3y^(2)-2lambdaxy+9x=0, C_(2):3x^(2)-4y^(2)+8xy-3x=0`A. `lambda=(4)/(3)`B. `lambda=12`C. `lambda=1`D. none of these

The value of `lambda` for which the lines joining the point of interse

1.	The value of `lambda` for which the lines joining the point of intersection of curves `C_(1)` and `C_(2)` to the origin are equally inclined to the axis of x. `C_(1):lambdax^(2)+3y^(2)-2lambdaxy+9x=0, C_(2):3x^(2)-4y^(2)+8xy-3x=0`A. `lambda=(4)/(3)`B. `lambda=12`C. `lambda=1`D. none of these
Answer» Correct Answer - B The combined equation of the striaght lines joining the origin to the points of intersecton of `C_(1)` and `C_(2)` is a homogeneous equation and is given by `lambdax^(2)+3y^(3)-2lambdaxy+3(3x^(2)-4y^(2)+8xy)=0` `or, (lambda+9)x^(2)+2xy(12-lambda)-9y^(2)=0`. Lines given by this equation are equally inclined with X-axis. `therefore" Sum of their slopes = 0 "` `rArr" "(-2(12-lambda))/(-9)=0" "[becausem_(1)+m_(2)=-(2h)/(b)]` `rArr" "lambda=12`

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