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JEE Main2005MathematicsThree Dimensional GeometryActual

The line parallel to the x -axis and passing through the intersection of the lines ax +2 b y+3 b=0 and b x-2 a y-3 a=0 , where (a, b) (0,0) is

Options

  1. Abelow the x -axis at a distance of 3 2 from it
  2. Bbelow the x -axis at a distance of 2 3 from it
  3. Cabove the x -axis at a distance of 3 - from it
  4. Dabove the x -axis at a distance of 2 3 from it

Correct answer

A. below the x -axis at a distance of 3 2 from it

Step-by-step solution

aligned & a x+2 b y+3 b+ (b x-2 a y-3 a)=0 & (a+b ) x+(2 b-2 a ) y+3 b-3 a=0 & a+b =0 =-a / b & a x+2 b y+3 b- a b (b x-2 a y-3 a)=0 & a x+2 b y+3 b-a x+ 2 a^2 b y+ 3 a^2 b =0 & y (2 b+ 2 a^2 b )+3 b+ 3 a^2 b =0 & y ( 2 b^2+2 a^2 b )=- ( 3 b^2+3 a^2 b ) & y= -3 (a^2+b^2 ) 2 (b^2+a^2 ) = -3 2 & aligned y=- 3 2 so it is 3 / 2 units below x -axis.

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