If the ratio of the lengths of tangents drawn from the point $(f,g)$ to the given circle ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} + 3x + 3y = 0$ be $2 : 1$, then

  • A

    ${f^2} + {g^2} + 2g + 2f + 2 = 0$

  • B

    ${f^2} + {g^2} + 4g + 4f + 4 = 0$

  • C

    ${f^2} + {g^2} + 4g + 4f + 2 = 0$

  • D

    None of these

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