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Homogenization

The equation ...

Question

The equation of the lines represented by $4 x^{2} + 24 x y + 11 y^{2} = 0$ is/are

A

2 x + y = 0

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B

2 x + 11 y = 0

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C

x - y = 0

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D

y - 2 x = 0

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Solution

The correct option is B $2 x + 11 y = 0$
Factorising $4 x^{2} + 2 x y + 22 x y + 11 y^{2} = 0$
$\Rightarrow 2 x (2 x + y) + 11 y (2 x + y) = 0$
$\Rightarrow (2 x + 11 y) (2 x + y) = 0$

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