Chapter 9 Quadratic Relations and Conic Sections - 9.3 Graph and Write Equations of Circles - 9.3 Exercises - Skill Practice - Page 630: 37

$$ x^2+y^2=116$$

Since the center is at the origin, we use the distance formula to find that the radius must be: $$\sqrt{\left(4-0\right)^2+\left(-10-0\right)^2} \\ 2\sqrt{29}$$ Thus, it follows: $$x^2+y^2=r^2 $$ $$ x^2+y^2=116$$