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BITSAT2013MathematicsStraight LinesActual

If 4 a²+b²+2 c²+4 a b-6 a c-3 b c=0, the family of lines ax + by + c =0 is concurrent at one or the other of the two points-

Options

  1. A(-1,- 1 2 ),(-2,-1)
  2. B(-1,-1), (-2,- 1 2 )
  3. C(-1,2), ( 1 2 ,-1 )
  4. D(1,2), ( 1 2 ,-1 )

Correct answer

A. (-1,- 1 2 ),(-2,-1)

Step-by-step solution

array l 4 a²+b²+2 c²+4 a b-6 a c-3 b c (2 a+b)²-3(2 a+b) c+2 c²=0 (2 a+b-2 c)(2 a+b-c)=0 c=2 a+b or c=a+ 1 2 b array The equation of the family of lines is a(x+2)+b(y+1)=0 or a(x+1)+b (y+ 1 2 )=0 giving the point of concurrence (-2,-1) or (-1,- 1 2 )

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