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

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

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

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

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

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Solution

The correct option is C $y^{2} - x^{2} - 4 x - 4 = 0$
$y = | x - 2 | ⟹ y^{2} = x^{2} - 4 x + 4$
Image of any point $(h, k)$ in y-axis is $(- h, k)$
Now reflection of any point (h,k) of $y^{2} = x^{2} - 4 x + 4$ in y-axis is $(- h, k)$ and will result into new equation
$y^{2} = (- x)^{2} - 4 (- x) + 4 ⟹ y^{2} = x^{2} + 4 x + 4$

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