GIven:
center (-8, -1)
r = radius = 9
Using the formula for equation of circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex][tex]\begin{gathered} \text{center (h, k) = (-8, -1)} \\ h\text{ = -8, k=-1} \\ \\ \text{Inserting into the formula:} \\ \mleft(x-\mleft(-8\mright)\mright)^2+\mleft(y-\mleft(-1\mright)\mright)^2=9^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Multiplication of same sign gives positive sign} \\ (x+8)^2+(y+1)^2=9^2 \\ \\ \text{The equation:} \\ (x+8)^2+(y+1)^2=81 \end{gathered}[/tex]