Chapter 9 Quadratic Relations and Conic Sections - 9.3 Graph and Write Equations of Circles - 9.3 Exercises - Skill Practice - Page 630: 58

See below

From geometry, a line tangent to a circle is perpendicular to the radius at the point of tangency. The radius with endpoint $(15,5)$ has slope $m=\frac{0-5}{0-15}=\frac{1}{3}$, so the slope of the tangent line at $(15, 5)$ is the negative reciprocal of $-3$. An equation of the tangent line is as follows: $$y-5=-3(x-15)\\y=-3x+50$$