Answer
$x^2+y^2=25$
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, $(
-3,4
),$ is on the circle, then substitute these coordinates into the $x$ and $y$ variables, respectively, of the equation above. That is,
\begin{array}{l}\require{cancel}
(-3)^2+(4)^2=r^2
\\\\
9+16=r^2
\\\\
r^2=25
.\end{array}
Using the given center and the solved radius, the equation of the circle is $
x^2+y^2=25
.$
