Answer
$(x-\sqrt{5})^2+(y+\sqrt{7})^2=3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Center-Radius Form to find the equation of the circle with the following characteristics:
\begin{array}{l}\require{cancel}
\text{center }
(\sqrt{5},-\sqrt{7})
,\text{ radius }
\sqrt{3}
.\end{array}
$\bf{\text{Solution Details:}}$
With the given center, then $h=
\sqrt{5}
$ and $k=
-\sqrt{7}
.$ With the given radius, then $r=
\sqrt{3}
.$
Using the Center-Radius Form of the equation of circles which is given by $(x-h)^2+(y-k)^2=r^2,$ then the equation of the circle is
\begin{array}{l}\require{cancel}
(x-\sqrt{5})^2+(y-(-\sqrt{7}))^2=(\sqrt{3})^2
\\\\
(x-\sqrt{5})^2+(y+\sqrt{7})^2=3
.\end{array}
