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

  • question_answer
    If the pair of lines \[a{{x}^{2}}+2(a+b)xy+b{{y}^{2}}=0\] lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then                                              [AIEEE 2005]

    A)            \[3{{a}^{2}}+10ab+3{{b}^{2}}=0\]                                  

    B)            \[3{{a}^{2}}+2ab+3{{b}^{2}}=0\]

    C)            \[3{{a}^{2}}-10ab+3{{b}^{2}}=0\]                                    

    D)            \[3{{a}^{2}}-2ab+3{{b}^{2}}=0\]

    Correct Answer: B

    Solution :

               Angle between the given lines is                    \[\tan \frac{\pi }{4}=\frac{2\sqrt{{{(a+b)}^{2}}-ab}}{a+b}\]                    Þ \[\frac{2\sqrt{{{(a+b)}^{2}}-ab}}{a+b}=1\] Þ \[3{{a}^{2}}+2ab+3{{b}^{2}}=0\]

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