Chapter 9 Quadratic Relations and Conic Sections - 9.3 Graph and Write Equations of Circles - 9.3 Exercises - Skill Practice - Page 630: 56

See below

From geometry, a line tangent to a circle is perpendicular to the radius at the point of tangency. The radius with endpoint $(-6,-2)$ has slope $m=\frac{0+2}{0+6}=\frac{1}{3}$, so the slope of the tangent line at $(-6, -2)$ is the negative reciprocal of $-3$. An equation of the tangent line is as follows: $$y+2=-3(x+6)\\y=-3x-20$$