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Keeping coordinate axes parallel, the origin is shifted to a point $(1, - 2)$ the transformed equation of $x^{2} + y^{2} = 2$ is

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$x^{2} + y^{2} - 2 x - 4 y + 3 = 0$

$x^{2} + y^{2} + 2 x - 4 y + 3 = 0$

$x^{2} + y^{2} + 2 x + 4 y + 3 = 0$

$x^{2} + y^{2} - 2 x + 4 y + 3 = 0$

answer is A.

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Detailed Solution

$x = X + 1 y = Y - 2 \Rightarrow {(X + 1)}^{2} + {(Y - 2)}^{2} = 2 \Rightarrow X^{2} + Y^{2} + 2 X - 4 Y + 3 = 0$

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