Distance between the two lines represented by the line $x^{2} + y^{2} + 2 x y + 2 x + 2 y = 0$ is:

\sqrt{2}

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\sqrt{5}

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2 \sqrt{5}

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none

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Solution

The correct option is B $\sqrt{2}$
$x^{2} + y^{2} + 2 x y + 2 x + 2 y = 0 x^{2} + x y + 2 x + y^{2} + x y + 2 y = 0 x (x + y + 2) + y (x + y + 2) = 0 (x + y) (x + y + 2) = 0 x + y = 0 x + y + 2 = 0$
The distance between the parallel lines is given as $\frac{| 2 - 0 |}{\sqrt{1^{2} + 1^{2}}} \frac{2}{\sqrt{2}} = \sqrt{2}$

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