Given:
The center of the circle is, (h, k) = (-4, -5)
The radius of the circle is, r =√2.
The general equation for a circle is given by,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the values, we have,
[tex]\begin{gathered} (x-(-4))^2+(y-(-5))^2=(\sqrt[]{6})^2 \\ (x+4)^2+(y+5)^2=6 \end{gathered}[/tex]