Answer
$(x+1)^2+(y+3)^2=34$
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 $(
-1,-3
)$ is
\begin{array}{l}\require{cancel}
(x-(-1))^2+(y-(-3))^2=r^2
\\\\
(x+1)^2+(y+3)^2=r^2
.\end{array}
Since the given point, $(
-4,2
),$ is on the circle, then substitute these coordinates into the $x$ and $y$ variables, respectively, of the equation above.
\begin{array}{l}\require{cancel}
(-4+1)^2+(2+3)^2=r^2
\\\\
(-3)^2+(5)^2=r^2
\\\\
9+25=r^2
\\\\
r^2=34
.\end{array}
Using the given center and the solved radius, the equation of the circle is $
(x+1)^2+(y+3)^2=34
.$