Statement- 1: If the general equation x^ 2 +y^ 2 +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 x^ 2 +2 h x y+b y^ 2 +2 g x+2 f y+c=0 represents pair of real lines if a b c+2 f g h-a f^ 2 -b g^ 2 -c h^ 2 =0
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 1^ 2 =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
Related: Mathematics — Pair of Lines · All PYQ Banks