St a t e m e n t − 1 : If the general equation x 2 + y 2 + 2 x y + 2 gx + 2 f y + 4 = 0 represents a pair of real lines then ∣ g ∣ ≥ 2 . St a t e m e n t − 2 : The equation a x 2 + 2 h x y + b y 2 + 2

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St a t e m e n t − 1 : If the general equation x 2 + y 2 + 2 x y + 2 gx + 2 f y + 4 = 0 represents a pair of real lines then ∣ g ∣ ≥ 2 . St a t e m e n t − 2 : The equation a x 2 + 2 h x y + b y 2 + 2 gx + 2 f y + c = 0 represents pair of real lines if ab c + 2 f g h − a f 2 − b g 2 − c h 2 = 0

TestHub · Accepted Answer

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

Mathematics - Pair of Lines Question with Solution | TestHub

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