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COMEDK2019MathematicsPair of Lines

If 3 x²+x y-y²-3 x+6 y+k=0 represents a pair of lines, then k=

Options

  1. A0
  2. B9
  3. C1
  4. D-9

Correct answer

D. -9

Step-by-step solution

If 3 x²+x y-y²-3 x+6 y+k=0 represents a pair of lines, then aligned | array ccc 3 & 1 2 & -3 2 1 2 & -1 & 3 -3 2 & 3 & k array |=0 3(-k-9)- 1 2 ( 1 2 k+ 9 2 )- 3 2 ( 3 2 - 3 2 ) &=0 -3 k-27- 1 4 k- 9 4 &=0 - 13 4 k- 117 4 &=0 &=-9 aligned

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