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AP EAMCET2010MathematicsStraight Lines

If a straight line L is perpendicular to the line 4 x-2 y=1 and forms a triangle of area 4 sq unit with the coordinate axes, then the equation of the line L is

Options

  1. A2 x+4 y+7=0
  2. B2 x-4 y+8=0
  3. C2 x+4 y+8=0
  4. D4 x-2 y-8=0

Correct answer

C. 2 x+4 y+8=0

Step-by-step solution

A straight line L is perpendicular to the line 4 x-2 y=1 therefore the equation of the line is x+2 y+ =0 (i) Also, the line (i) form a of area 4 unit ^2 with the coordinate axes, then 1 2 | array ccc 0 & 0 & 1 - & 0 & 1 0 & - / 2 & 1 array |=4(- )(- / 2)=8 ^2=16 =4 From Eq. (i) x+2 y+4=0 or 2 x+4 y+8=0

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