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The combined equation of straight lines that can be obtained by reflecting the lines $y = |x - 2|$ in the y-axis is

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$y^{2} + x^{2} + 4 x + 4 = 0$

$y^{2} + x^{2} - 4 x + 4 = 0$

$y^{2} - x^{2} + 4 x - 4 = 0$

$y^{2} - x^{2} - 4 x - 4 = 0$

answer is D.

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Detailed Solution

If we reflect $y = |x - 2|$ in y-axis, it will becomes $y = | - x - 2 | = | x + 2 | .$ The reflected lines are $y = x + 2, y = - x - 2$ . Their combined equation is $(y - x - 2) (y + x + 2) = 0$
$\Rightarrow y^{2} - {(x + 2)}^{2} = 0$

$\Rightarrow y^{2} - x^{2} - 4 x - 4 = 0$

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