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

  • question_answer
    If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then c has the value [AIEEE 2004]

    A)            - 2  

    B)            - 1

    C)            2    

    D)            1

    Correct Answer: C

    Solution :

               Given pair of lines is \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\]            Given, \[{{m}_{1}}+{{m}_{2}}=4{{m}_{1}}{{m}_{2}}\Rightarrow \frac{-2c}{7}=\frac{-4}{7}\Rightarrow c=2\] \[\left[ \because \ {{m}_{1}}+{{m}_{2}}=-\frac{2h}{b}=\frac{-2c}{7};\ {{m}_{1}}{{m}_{2}}=\frac{-1}{7} \right]\]


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