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A line is drawn through the point (1, 2)...

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

A

`-(1)/(4)`

B

-4

C

-2

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
(y-2) = m(x-1)
`therefore OP = 1-(2)/(m)`
OQ = 2-m

Area of `DeltaPOQ`
`=(1)/(2) (OP)(OQ)=(1)/(2)(1-(2)/(m))(2-m)`
`=(1)/(2)[2-m-(4)/(m)+2]`
`=(1)/(2)[4-(m+(4)/(m))]`
`=(1)/(2)[(sqrt(-m)-(2)/(sqrt(-m)))^(2)+8] " "(because m lt 0)`
Which has least value when m =-2.
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