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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2002

  • question_answer
    If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\]represents a pair of lines, then the value of k is:

    A)  9                                            

    B)  1

    C) \[-9\]                                    

    D)  zero

    Correct Answer: C

    Solution :

    The given equation represents a pair of lines \[abc+2ghf-a{{f}^{2}}-h{{g}^{2}}-c{{h}^{2}}=0\] \[3(-1)k+2(3)-(-3)(1/2)-3({{3}^{2}})\] \[-(-1)-{{\left( -\frac{3}{2} \right)}^{2}}-k{{\left( \frac{1}{2} \right)}^{2}}=0\] \[-3k-\frac{9}{2}-27+\frac{9}{4}-\frac{k}{4}=0\] \[-12k-18-108+9-k=0\] \[\Rightarrow \]               \[-13k=117\] \[k=-9\]


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