$x^{2} + 4 y^{2} = 4 x y$ , then $x : y$ is

2 : 1

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1 : 2

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1 : 1

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1 : 4

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Solution

The correct option is A $2 : 1$
$x^{2} + 4 y^{2} = 4 x y$
$x^{2} - 4 x y + 4 y^{2} = 0$
$⟹ {(\begin{matrix} x - 2 y \end{matrix})}^{2} = 0$
$⟹ x = 2 y$
$⟹ \frac{x}{y} = \frac{2}{1}$

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