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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

  • question_answer
    The equation\[2{{x}^{2}}+4x-k{{y}^{2}}+4x+2y-1=0\]represents a pair of lines. The value of \[k\] is:

    A)  \[-5/3\]                              

    B)  \[+\,5/3\]

    C)  \[1/3\]                                

    D) \[-1/3\]

    Correct Answer: A

    Solution :

     Equation   of   a   pair   of   lines\[2{{x}^{2}}+4xy-k{{y}^{2}}+4x+2y-1=0\] the standard equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\]and comparing \[a=2,\,b=-k,\,f=1,\] \[g=2,c=-1\]and \[h=2.\] Hence equation represents a pair of lines, therefore \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\]\[\Rightarrow \]\[2k+8-2+4k+4=0\Rightarrow 6k=-10\] \[k=-5/3\]


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