A line is drawn through the point (1, 2) to meet the coordinates 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 :

Engineering

Mathematics

Various Form of a Straight Line

Question

–4

$\frac{- 1}{4}$

$\frac{- 1}{2}$

–2

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$∴ Area = | \frac{1}{2} (1 - \frac{2}{m}) (2 - m) |$

$= \frac{1}{2} {m - 4 + \frac{4}{m}}$

$\frac{dA}{dx} = 0$

Gives m² = 4 Þ m = ± 2

$∴$ Area m = – 2.