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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • 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

    A)  1                                            

    B)  \[-1\]

    C)  2                                            

    D)  \[-2\]

    Correct Answer: C

    Solution :

                    The given pair of lines is \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] On comparing with \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\] we get \[a=1,2h=-2c,b=-7\] \[{{m}_{1}}+{{m}_{2}}=-\frac{2h}{b}=-\frac{2c}{7}\]and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}=-\frac{1}{7}\] Given that, \[{{m}_{1}}+{{m}_{2}}=4{{m}_{1}}{{m}_{2}}\] \[\Rightarrow \]               \[-\frac{2c}{7}=-\frac{4}{7}\Rightarrow c=\frac{4}{2}=2\]


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