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
    Angle between the lines represented by the equation \[{{x}^{2}}+2xy\sec \theta +{{y}^{2}}=0\] is

    A)            \[\theta \]                             

    B)            \[2\theta \]

    C)            \[\frac{\theta }{2}\]          

    D)            None of these

    Correct Answer: A

    Solution :

               Let angle between both the lines is \[\alpha \], then            \[\alpha ={{\tan }^{-1}}\left( \frac{2\sqrt{{{h}^{2}}-ab}}{a+b} \right)={{\tan }^{-1}}\left( \frac{2\sqrt{{{\sec }^{2}}\theta -1}}{1+1} \right)=\theta \] .


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