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(D) The equation of the chord of contact for a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ from an external point $(x_1, y_1)$ is given by $T = 0$,where $T

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$4x + 9y = 0$

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(D) The equation of the chord of contact for a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ from an external point $(x_1, y_1)$ is given by $T = 0$,where $T = xx_1 + yy_1 + g(x + x_1) + f(y + y_1) + c = 0$.Given the circle $x^2 + y^2 + 4x + 6y - 12 = 0$,we have $g = 2$,$f = 3$,and $c = -12$.The point is $(x_1, y_1) = (2, 3)$.Substituting these values into the formula:$x(2) + y(3) + 2(x + 2) + 3(y + 3) - 12 = 0$$2x + 3y + 2x + 4 + 3y + 9 - 12 = 0$$4x + 6y + 1 = 0$$4x + 6y = -1$Since none of the provided options match this result,the correct answer is none of these.

The equation of the chord of contact of the circle $x^2 + y^2 + 4x + 6y - 12 = 0$ with respect to the point $(2, 3)$ is:

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