The general equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) = coordinates of the center of the circle
r = radius of the circle
Now, the equation given in the question, which is:
[tex](x+5)^2+(y-4)^2=9[/tex]
Can be re-written as follows:
[tex]\begin{gathered} (x+5)^2+(y-4)^2=9 \\ \Rightarrow(x-(-5))^2+(y-4)^2=3^2 \end{gathered}[/tex]
Now, we can easily compare the resulting expression with the general equation of a circle.
On doing so, we have that:
(a, b) = (-5, 4)
r = 3
Thus, the center of the circle is (-5, 4) and the radius is 3
Therefore, the correct answer is: Option C
