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

  • question_answer
    The values of h for which the equation \[3{{x}^{2}}+2hxy-3{{y}^{2}}-40x+30y-75=0\] represents a pair of straight lines, are [MP PET 1989]

    A)            4, 4 

    B)            4, 6

    C)            4, - 4                                          

    D)            0, 4

    Correct Answer: A

    Solution :

               We have \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\]                    \[\Rightarrow (3)(-3)(-75)+2(15)(-20)(h)\]                                                 \[-3{{(15)}^{2}}-(-3){{(-20)}^{2}}-(-75){{h}^{2}}=0\]                    \[\Rightarrow 675-600h-675+1200+75{{h}^{2}}=0\]\[\Rightarrow h=4,4.\]


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