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(C) The equation of the circle is $x^2 + y^2 - 6x - 8y - 11 = 0$. Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -3$

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$19$

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(C) The equation of the circle is $x^2 + y^2 - 6x - 8y - 11 = 0$. Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -3$ and $f = -4$. The center of the circle is $C(-g, -f) = (3, 4)$. The radius of the circle is $r = \sqrt{g^2 + f^2 - c} = \sqrt{(-3)^2 + (-4)^2 - (-11)} = \sqrt{9 + 16 + 11} = \sqrt{36} = 6$. The distance between the point $P(15, 9)$ and the center $C(3, 4)$ is $CP = \sqrt{(15 - 3)^2 + (9 - 4)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$. The largest distance from point $P$ to the circle is given by $CP + r = 13 + 6 = 19$.

The largest among the distances from the point $P(15, 9)$ to the points on the circle $x^2 + y^2 - 6x - 8y - 11 = 0$ is

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