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KCET2013MathematicsStraight Lines

The minimum area of the triangle formed by the variable line 3 x+4 y=12 and the coordinate axes is

Options

  1. A144
  2. B25 2
  3. C49 4
  4. D12

Correct answer

D. 12

Step-by-step solution

Given equation of line is x 3 +4 y=12 (4 / ) + y (3 / ) =1...(i) It intereset the coordinate axes at A ( 4 , 0 ) and B (0, 3 ) . Area of O A B , aligned &= 1 2 4 3 &= 12 2 ...(ii) aligned Now, for area to be minimum, 2 should be maximum i.e., 2 =1 ( | 2 | 1) Minimum area _ = 12 1 =12

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