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A straight line l with negative slope pa...

A straight line l with negative slope passes through (8,2) and cuts the coordinate axes at P and Q. Find absolute minimum value of ''OP+OQ`` where O is the origin-

Text Solution

Verified by Experts

The correct Answer is:
18
Let the equation of line be (y-2) = m(x-8) where `m lt 0.`
`rArr P-= (8-(2)/(m), 0)" and " Q -=(0 ,2-8m)`
`"Now, "OP+OQ =|8-(2)/(m)| + |2 -8m|`
`= 10+(2)/(-m) + (-8m)`
`ge 10+2sqrt((2)/(-m) xx(-8m)) ge 18`
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Knowledge Check

  • 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
    10
    B
    18
    C
    16
    D
    112

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