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AP EAMCET2008MathematicsPair of Lines

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

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

C. 2

Step-by-step solution

Given pair of lines is x^2-10 x y+12 y^2+5 x-16 y-3=0 On comparing with a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 we get, a= , h=-5, b=12, g= 5 2 , f=-8, c=-3 Condition for represents a pair of lines is aligned & a b c+2 f g h-a f^2-b g^2-c h^2=0 & 12 (-3)+2(-8) ( 5 2 )(-5)- (-8)^2 & -12 ( 5 2 )^2+3(-5)^2=0 & -36 +200-64 -75+75=0 & 100 =200 =2 & aligned

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