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KCET2008MathematicsPair of Lines

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

Options

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

Correct answer

D. -9

Step-by-step solution

Given equation is 3 x²+x y-y²-3 x+6 y+k=0 Here a =3, ~b =-1, ~h = 1 2 , ~g =- 3 2 , f =3, c = k To represent a pair of lines, aligned & abc +2 fgh - af ²- bg ²- ch ²=0 & 3(-1)( k )+2 3 (- 3 2 ) 1 2 & -3(3)²+1 ( -3 2 )²- k ( 1 2 )²=0 & -3 k - 9 2 -27+ 9 4 - k 4 =0 & -13 k 4 - 117 4 =0 & k =-9 aligned

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