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BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
    A   family   of   lines   is   given   by \[(1+2\lambda )x+(1-\lambda )y+\lambda =0,\,\lambda \] being the parameter. The line belonging to this family at the maximum distance from the point\[(1,4)\]is

    A)  \[4x-y+1=0\]       

    B)         \[33x+12y+7=0\]               

    C)         \[12x+33y=7\]    

    D)         None of these

    Correct Answer: C

    Solution :

    Here, \[x+y+\lambda (2x-y+1)=0\] Since, each line passes through the point of intersection of the lines. \[x+y=0\]and \[2x-y+1=0,\] which is \[(-1/3,1/3).\] \[\therefore \] Slope of the required line, \[m=\frac{-1}{\frac{4-1/3}{1+1/3}}=\frac{-4}{11}\]  \[\therefore \]The required line is \[y-\frac{1}{3}=-\frac{4}{11}\left( x+\frac{1}{3} \right)\]                 \[\Rightarrow \]    \[12x+33y=7\]


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