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(C) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$. Given $S = x^2 + y^2 + 2x + 2y + 1 =

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$3x^2 - 8xy + 3y^2 + 2x + 2y - 2 = 0$

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(C) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$. Given $S = x^2 + y^2 + 2x + 2y + 1 = 0$ and point $(1, 1)$. $S_1 = 1^2 + 1^2 + 2(1) + 2(1) + 1 = 1 + 1 + 2 + 2 + 1 = 7$. $T = x(1) + y(1) + (x + 1) + (y + 1) + 1 = 2x + 2y + 3$. Substituting these into $SS_1 = T^2$: $7(x^2 + y^2 + 2x + 2y + 1) = (2x + 2y + 3)^2$. $7x^2 + 7y^2 + 14x + 14y + 7 = 4x^2 + 4y^2 + 9 + 8xy + 12x + 12y$. Rearranging the terms: $3x^2 - 8xy + 3y^2 + 2x + 2y - 2 = 0$.

The equation of the pair of tangents drawn from the point $(1, 1)$ to the circle $x^2 + y^2 + 2x + 2y + 1 = 0$ is:

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