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straight line L with negative slope pass...

straight line L with negative slope passes through the point (9,4) cuts the positive coordinate axes at the point P and W As L. Varies, find the minimum value of |OP|+|OQ| , where O is origin .

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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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