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Q.

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

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a

28

b

15

c

18

d

10

answer is C.

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Detailed Solution

Let the equation of the line L bey−2=m(x−8),m<0 Coordinates of P and Q are P8−2m,0 and Q(0,2−8m) . so,OP+OQ=8−2m+2−8m =10+2−m+8(−m) ≥10+22−m×8(−m)≥18 absolute min . value of OP+OQ=18 .
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