SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The equation of a circle is given as :
[tex](x-a)^2+(y-b)^2=r^2[/tex]
comparing with the given equation:
[tex]\text{( x+5)}^2+(y-4)^2=9[/tex]
we have that:
[tex]\begin{gathered} \text{Centre ( a, b ) = ( -5, 4)} \\ and\text{ } \\ \text{Radius = }\sqrt[]{9}=\text{ 3} \end{gathered}[/tex]
CONCLUSION:
From the detailed explanation, we can see that the correct answer is:
[tex](-5,\text{ 4); r = 3 ( OPTION }C)[/tex]
