JEE Main & Advanced Mathematics Straight Line Question Bank Slope of line, Equation of line in different forms

  • question_answer
    The equations of the lines which pass through the origin and are inclined at an angle \[{{\tan }^{-1}}m\] to the line \[y=mx+c,\] are

    A)            \[x=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\]                                    

    B)            \[y=0,\ \ 2mx+({{m}^{2}}-1)\ y=0\]

    C)            \[y=0,\ \ 2mx+(1-{{m}^{2}})\ y=0\]                                    

    D)            None of these

    Correct Answer: B

    Solution :

               Angle between both the lines is                    \[{{\tan }^{-1}}m\pm {{\tan }^{-1}}m={{\tan }^{-1}}\frac{2m}{1-{{m}^{2}}}\] or\[{{\tan }^{-1}}0\]                    Therefore equation of lines are\[y=0\], \[y=\frac{2mx}{1-{{m}^{2}}}\].


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