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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

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

    A)  2                                            

    B)  \[-2\]                   

    C)  \[-5\]                   

    D)         5

    E)  3

    Correct Answer: E

    Solution :

    In given equation \[a=k,h=-1,b=-1,g=-1,f=1,c=0\] So, given equation represents a pair of lines, if \[\left| \begin{matrix}    k & -1 & -1  \\    -1 & -1 & 1  \\    -1 & 1 & 0  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[k(-1)+1(0+1)-1(-1-1)=0\] \[\Rightarrow \]               \[-k+1+2=0\] \[\Rightarrow \]                               \[k=3\]


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