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
    The angle between the lines \[{{x}^{2}}+4xy+{{y}^{2}}=0\] is [Karnataka CET 2001; Pb. CET 2001]

    A)            \[{{60}^{o}}\]                       

    B)            \[{{15}^{o}}\]

    C)            \[{{30}^{o}}\]                       

    D)            \[{{45}^{o}}\]

    Correct Answer: A

    Solution :

               Comparing the given equation with the standard equation, we get \[a=1,\,h=2\]and \[b=1.\]            We also know that relation for the angle between the lines  \[(\theta )\] is \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{a+b}\]            \\[\tan \theta =\frac{2\sqrt{{{2}^{2}}-1}}{1+1}=\sqrt{3}\] or\[\theta ={{\tan }^{-1}}(\sqrt{3})={{60}^{o}}\].


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