Find the equation of the circle

The distance between the center and the tangent line is equal to the radius.

Thus,

$r = \frac{\mid ax_{0} + by_{0} + c \mid}{\sqrt{a^{2} + b^{2}}}$

Subtituting $a = 1, b = -3, c = -9, x_{0} = 2$ , and $y_{0} = 1$ ,

$r = \frac{\mid (1)(2) + (-3)(1) -9 \mid}{\sqrt{(1)^{2} + (-3)^{2}}}$

$r = \sqrt{10}$ .

Substituting in $(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$ yields

$(x - 2)^{2} + (y - 1)^{2} = (\sqrt{10})^{2}$

$x^{2} + y^{2} - 4x -2y - 5 = 0$