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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

  • question_answer
    If the lines joining origin to the points of intersection of the line \[fx-gy=\lambda \] and the curve \[{{x}^{2}}+hxy-{{y}^{2}}+gx+fy=0\] be mutually perpendicular, then

    A)            \[\lambda =h\]                   

    B)            \[\lambda =g\]

    C)            \[\lambda =fg\]                  

    D)            \[\lambda \]may have any value

    Correct Answer: D

    Solution :

               Making the equation of curve homogeneous with the help of equation of line \[\frac{fx-gy}{\lambda }=1\]and to be perpendicular to both the lines represented by this homogeneous equation            \[a+b=0\Rightarrow \lambda +gf-\lambda -gf=0\Rightarrow 0=0\]            Hence, \[\lambda \]may have any value.


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