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JEE Main 2012Offline
Exam
JEE Main
Year
2012
Mode
Offline
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2012 · Offline · Mathematics · Straight Lines

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

A line is drawn through the point (1,2)(1,2) to meet the coordinate axes at PP and QQ such that it forms a triangle OPQOPQ, where OO is the origin. If the area of the triangle OPQOPQ is least, then the slope of the line PQPQ is

Options

  1. A−14-\frac{1}{4}
  2. B−4-4
  3. C−2-2
  4. D−12-\frac{1}{2}

Correct answer

C. −2-2

Step-by-step solution

Equation of line passing through (1,2)(1,2) with slope mm is y−2=m(x−1)y-2=m(x-1) Area of ΔOPQ=(m−2)22∣m∣\Delta \mathrm{OPQ}=\frac{(m-2)^2}{2|m|} Δ=m2+4−4m2mΔ=m2+2m−2\Delta=\frac{m^2+4-4 m}{2 m} \quad \Delta=\frac{m}{2}+\frac{2}{m}-2 Δ\Delta is least if m2=2m⇒m2=4⇒m=±2⇒m=−2\frac{m}{2}=\frac{2}{m} \quad \Rightarrow m^2=4 \quad \Rightarrow m=\pm 2 \quad \Rightarrow m=-2
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