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 o

Question

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

TestHub · Accepted Answer

Equation of line passing through ( 1 , 2 ) with slope m is y − 2 = m ( x − 1 ) Area of Δ OPQ = 2∣ m ∣ ( m − 2 ) 2 ​ Δ = 2 m m 2 + 4 − 4 m ​ Δ = 2 m ​ + m 2 ​ − 2 Δ is least if 2 m ​ = m 2 ​ ⇒ m 2 = 4 ⇒ m = ± 2 ⇒ m = − 2

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