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AP EAMCET2009MathematicsPair of Lines

The value of with | | < 16 such that 2 x^2-10 x y+12 y^2+5 x+ y-3=0 represents a pair of straight lines, is

Options

  1. A-10
  2. B-9
  3. C10
  4. D9

Correct answer

B. -9

Step-by-step solution

Given equation is 2 x^2-10 x y+12 y^2+5 x+ y-3=0 Here, a=2, h=-5, b=12, g= 5 2 , f= 2 , c=-3 For pair of lines | array lll a & h & g h & b & f g & f & c array |=0 array cc & | array rrr 2 & -5 & 5 / 2 -5 & 12 & / 2 5 / 2 & / 2 & -3 array |=0 & 2 (-36- ^2 4 )+5 (15- 5 4 ) & + 5 2 ( -5 2 -30 )=0 & -72- ^2 2 +75- 25 4 - 25 4 -75=0 & ^2+25 +144=0 & ( +9)( +16)=0 & =-9 ( | | < 16) array

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