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JEE Main & Advanced Mathematics Straight Line Question Bank Self Evaluation Test - Straight Lines & Pair Striaght Lines

  • question_answer
    A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points P and Q. as L varies the absolute minimum value of \[OP+OQ\] is (O is origin)

    A) 28

    B) 15

    C) 18

    D) 10

    Correct Answer: C

    Solution :

    [c] Let the equation of the line L be \[y-2=m(x-8),m<0\] Coordinates of P and Q are \[P\left( 8-\frac{2}{m},0 \right)\] and \[Q(0,2-8m).\] So, \[OP+OQ=8-\frac{2}{m}+2-8m\] \[=10+\frac{2}{-m}+8(-m)\] \[\ge 10+2\sqrt{\frac{2}{-m}\times 8(-m)}\ge 18\] absolute min. value of \[OP+OQ=18.\]


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