Answer
$(x+4)^2+(y-1)^2=20$
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 $(
-4,1
)$ is
\begin{array}{l}\require{cancel}
(x-(-4))^2+(y-1)^2=r^2
\\\\
(x+4)^2+(y-1)^2=r^2
.\end{array}
Since the given point, $(
-2,5
),$ is on the circle, then substitute these coordinates into the $x$ and $y$ variables, respectively, of the equation above.
\begin{array}{l}\require{cancel}
(-2+4)^2+(5-1)^2=r^2
\\\\
(2)^2+(4)^2=r^2
\\\\
4+16=r^2
\\\\
r^2=20
.\end{array}
Using the given center and the solved radius, the equation of the circle is $
(x+4)^2+(y-1)^2=20
.$
