A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is (1) `-1/4` (2) `-4` (3) `-2` (4) `-1/2`

Explanation

Line PQ

`(y-2)=m(x-1)`

If x=0 then y=2-m

if y=0 then x=`1-2/m`

Area of `/_OPQ=1/2(2-m)((m-2)/m)`

after differentiate with respect to m

`(deltaA)/(deltam)=delta/(deltam)(-1/2(m-2)^2/m)`

putting`(deltaA)/(deltam)=0` and solving it we get

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