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MHT CET2012MathematicsStraight Lines

If 2 a+b+3 c=0 , then the line a x+b y+c=0 passes through the fixed point that is

Options

  1. A( 2 3 , 1 3 )
  2. B(0,1)
  3. C( 2 3 , 0 )
  4. DNone of these

Correct answer

A. ( 2 3 , 1 3 )

Step-by-step solution

Given, 2 a+b+3 c+0 ...(i) and line, a x+b y+c=0 3 a x+3 b y+3 c=0 ...(ii) On subtracting Eq. (i) from Eq. (ii), we get (3 x-2) a+(3 y-1) b=0 a+0 b On comparing both sides, we get 3 x-2=0 x= 2 3 and 3 y-1=0 y= 1 3 Line, a x+b y+c=0 passes through the fixed point ( 2 3 , 1 3 ) .

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