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

Options

A. `-(1)/(4)`
B. -4
C. -2
D. `-(1)/(2)`

Answer

C

Explanation

(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.