Answer
$x^2+y^2=221$
Work Step by Step
Using $(x-h)^2+(y-k)^2=r^2$ or the Center-Radius form of the equation of circles, the equation of the circle with center $(
0,0
)$ is
\begin{array}{l}\require{cancel}
(x-0)^2+(y-0)^2=r^2
\\\\
x^2+y^2=r^2
.\end{array}
Since the given point, $(
11,-10
),$ is on the circle, then substitute these coordinates into the $x$ and $y$ variables, respectively, of the equation above.
\begin{array}{l}\require{cancel}
(11)^2+(-10)^2=r^2
\\\\
121+100=r^2
\\\\
r^2=221
.\end{array}
Using the given center and the solved radius, the equation of the circle is $
x^2+y^2=221
.$
