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BITSAT2016MathematicsPair of LinesActual

The equation x²-2 3 x y+3 y²-3 x+3 3 y-4=0 represents

Options

  1. Aa pair of intersecting lines
  2. Ba pair of parallel lines with distance between them 5 2
  3. Ca pair of parallel lines with distance between them 5 2
  4. Da conic section, which is not a pair of straight lines

Correct answer

B. a pair of parallel lines with distance between them 5 2

Step-by-step solution

We have a=1, h=- 3 , b=3, g=- 3 2 , f = 3 3 2 , c =-4 Thus a b c+2 f g h-a f²-b g²-c h²=0 Hence the equation represents a pair of straight lines. Again a h = h b = g f =- 1 3 the lines are parallel. The distance between them =2 g²-a c a(a+b) =2 9 4 +4 1(1+3) = 5 2

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