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Algebra of Limits

Determine the...

Question

Determine the nature of line represented by $4 x^{2} + 4 x y + y^{2} = 0$ .

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Solution

$4 x^{2} + 4 x y + y^{2} = 0 n a t u r e o f l i n e s b y f a c t o r i s a t i o n m e t h o d \Rightarrow 4 x^{2} + 2 x y + 2 x y + y^{2} \Rightarrow 2 x (2 x + y) + y (2 x + y) = 0 \Rightarrow (2 x + y) (2 x + y) = 0 ∴ 2 x + y = 0 a n d 2 x + y = 0 I t i s p a i r s o f s t r a i g h t$

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