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Q.

A straight line L with negative slope passes through the point (1, 1) and cuts the positive coordinate axes at the points A and B. If O is the origin, then the minimum value of OA + OB as L varies, is ……

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answer is 4.

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Detailed Solution

Let m be the slope of line L where m<0.

Equation of L is y−1=m(x−1)⇒−mx+y=1−m⇒OA=1−m−m,OB=1−m

OA+OB= 1−m−m+1−m=2−m+1m≥4.           ∴Minimum value of OA + OB is 4

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