JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Critical Thinking

  • question_answer The angle between the pair of straight lines \[{{y}^{2}}{{\sin }^{2}}\theta -xy{{\sin }^{2}}\theta +{{x}^{2}}({{\cos }^{2}}\theta -1)=1,\]is [MNR 1985; UPSEAT 2000; Kerala (Engg.) 2005]

    A)            \[\frac{\pi }{3}\]                 

    B)            \[\frac{\pi }{4}\]

    C)            \[\frac{2\pi }{3}\]               

    D)            None of these

    Correct Answer: D

    Solution :

               \[\alpha ={{\tan }^{-1}}\left\{ \frac{2\sqrt{\frac{{{\sin }^{2}}\theta }{4}-{{\sin }^{2}}\theta ({{\cos }^{2}}\theta -1)}}{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -1} \right\}\]                       \[={{\tan }^{-1}}\infty \Rightarrow \alpha =\frac{\pi }{2}\]

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