Explanation
We are to write the equation of the circle in standard form
Given theequation:
[tex]x^2+6x+y^2-4y=-9[/tex][tex]\left(x−a\right)^2+\left(y−b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)[/tex]
Using completing the square method
[tex]\left(x-\left(-3\right)\right)^2+\left(y-2\right)^2=2^2[/tex]
Thus, we will have the answer to be
[tex](x+3)^2+(y-2)^2=2^2[/tex]
Where
[tex]\begin{gathered} (a,b)=(-3,2) \\ r=2 \end{gathered}[/tex]
