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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of Pair of Straight Lines

  • question_answer
    Difference of slopes of the lines represented by equation \[{{x}^{2}}({{\sec }^{2}}\theta -{{\sin }^{2}}\theta )-2xy\tan \theta +{{y}^{2}}{{\sin }^{2}}\theta =0\]is [Kurukshetra CEE 2002]

    A)            4    

    B)            3

    C)            2    

    D)            None of these

    Correct Answer: C

    Solution :

               We know that \[{{m}_{1}}-{{m}_{2}}=\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4{{m}_{1}}{{m}_{2}}}\]            \[=\sqrt{{{\left( \frac{2\tan \theta }{{{\sin }^{2}}\theta } \right)}^{2}}-4\left( \frac{{{\sec }^{2}}\theta -{{\sin }^{2}}\theta }{{{\sin }^{2}}\theta } \right)}\]            \[=\sqrt{\frac{4{{\tan }^{2}}\theta }{{{\sin }^{4}}\theta }-4({{\sec }^{2}}\theta \,\text{cose}{{\text{c}}^{\text{2}}}\theta -1)}=2\].


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