If $\theta $ is the angle subtended at $P({x_1},{y_1})$ by the circle $S \equiv {x^2} + {y^2} + 2gx + 2fy + c = 0$, then

  • A

    $\cot \theta = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$

  • B

    $\cot \frac{\theta }{2} = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$

  • C

    $\tan \theta = \frac{{2\sqrt {{g^2} + {f^2} - c} }}{{\sqrt {{s_1}} }}$

  • D

    None of these

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