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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Angle between the pair of straight lines, Condition for parallel and perpendicular lines

  • question_answer
    If the angle between the lines represented by the equation \[{{y}^{2}}+kxy-{{x}^{2}}\]\[{{\tan }^{2}}A=0\]be \[2A\], then \[k=\]

    A)            0    

    B)            1

    C)            2    

    D)            \[\tan A\]

    Correct Answer: A

    Solution :

               Here \[\tan 2A=\frac{2\sqrt{\frac{{{k}^{2}}}{4}+{{\tan }^{2}}A}}{1-{{\tan }^{2}}A}\]            \[\Rightarrow \frac{2\tan A}{1-{{\tan }^{2}}A}=\frac{2\sqrt{\frac{{{k}^{2}}}{4}+{{\tan }^{2}}A}}{1-{{\tan }^{2}}A}\]            \[\Rightarrow \frac{{{k}^{2}}}{4}+{{\tan }^{2}}A={{\tan }^{2}}A\Rightarrow k=0\] .


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