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

A line is drawn through the point (1, 2) to meet the coordinate axesat

1.	A line is drawn through the point (1, 2) to meet the coordinate axesat P and Q such that it forms a triangle OPQ, where O is the origin. If thearea of the triangle OPQ is least, then the slope of the line PQ is(1) `-1/4`(2) `-4`(3) `-2`(4) `-1/2`
Answer» 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 `m^2=4` `m=pm2`

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

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