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JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. if the area of the triangle OPQ is least, then the slope of the line PQ is :   AIEEE  Solved  Paper-2012

    A) \[-\frac{1}{4}\]                                    

    B) \[-4\]

    C) \[-2\]                                       

    D) \[-\frac{1}{2}\]

    Correct Answer: C

    Solution :

                 \[(y-2)=m(x-1)\] \[OP=1-\frac{2}{m}\] \[OQ=2-m\] Area of \[\Delta POQ=\frac{1}{2}(OP)(OQ)=\frac{1}{2}\] \[\left( 1-\frac{1}{m} \right)(2-m)\]                    \[=\frac{1}{2}\left[ 2-m\frac{4}{m}+2 \right]\]                    \[=\frac{1}{2}\left[ 4-\left( m+\frac{4}{m} \right) \right]\] \[m=-2\]


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