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AP EAMCET2002MathematicsStraight Lines

If a straight line perpendicular to 2 x-3 y+7=0 forms a triangle with the co-ordinate axes whose area is 3 sq. units, then the equation of the straight line is :

Options

  1. A3 x+2 y= 2
  2. B3 x+2 y= 6
  3. C3 x+2 y= 4
  4. D3 x+2 y= 8

Correct answer

B. 3 x+2 y= 6

Step-by-step solution

The given line is 2 x-3 y+7=0 A perpendicular line to given line is 3 x+2 y+k=0 Put y=0 3 x+k=0 x=- k 3 Put x=0 0+2 y+k=0 y=- k 2 Area of the triangle O A B= 1 2 O A O B aligned & 3 & = 1 2 (- k 3 ) (- k 2 ) & k^2 & =36 k= 6 aligned Putting in (i) 3 x+2 y= 6

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