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

  • question_answer
    The gradient of one of the lines of \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is twice that of the other, then [MP PET 2000; Pb. CET 2002]

    A)            \[{{h}^{2}}=ab\]                 

    B)            \[h=a+b\]

    C)            \[8{{h}^{2}}=9ab\]             

    D)            \[9{{h}^{2}}=8ab\]

    Correct Answer: C

    Solution :

               Here, \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\]                    Given that \[{{m}_{1}}=2{{m}_{2}}\]                    \[\therefore \]\[3{{m}_{2}}=\frac{-2h}{b}\] and \[2m_{2}^{2}=\frac{a}{b}\]                    Þ \[2{{\left( \frac{-2h}{3b} \right)}^{2}}=\frac{a}{b}\]Þ \[8{{h}^{2}}=9ab\].


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