SATHEE: Straight Line Question 250

Straight Line Question 250

Question: 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)

Options:

A) 28

B) 15

C) 18

D) 10

Show Answer

Answer:

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( 8-\frac{2}{m},0 ) $ 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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Straight Line Question 250

Question: 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)

Options:

Answer:

Solution:

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