Statement- 1 : If the general equation x²+y²+2 x y+2 g x+2 f y+4=0 represents a pair of real lines then | g | 2 . Statement- 2 : The equation a x²+2 h x y+b y²+2 g x+2 f y+c=0 represents pair of real lines if a b c+2 f g h-a f²-b g²-c h²=0

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Correct answer: D. Statement -1 is true, Statement- 2 is false

The equation represents a pair of lines if 1 1 4+2 f g 1-1 f ²-1 g ²-4 1²=0 (f-g)²=0 f=g The equation becomes (x+y)²+2 g(x+y)+4=0 Which represents pair of parallel lines, which are real provided (2 ~g )²-4 4 1 0 | g | 2

Statement- 1 : If the general equation x²+y²+2 x y+2 g x+2 f y+4=0 represents a pair of real lines then | g | 2 . Statement- 2 : The equation a x²+2 h x y+b y²+2 g x+2 f y+c=0 represents pair of real lines if a b c+2 f g h-a f²-b g²-c h²=0

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