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 :
![(x-a)^2+(y-b)^2=r^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/ilekd9w5v3ytefhk3unvr8rhka2u3mptc6.png)
comparing with the given equation:
![\text{( x+5)}^2+(y-4)^2=9](https://img.qammunity.org/2023/formulas/mathematics/college/hnnkhtz2vrw3t0c7ugkcyqm18vzbqn5rs8.png)
we have that:
![\begin{gathered} \text{Centre ( a, b ) = ( -5, 4)} \\ and\text{ } \\ \text{Radius = }\sqrt[]{9}=\text{ 3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/3soe9ace23piormaajzhiojjz8e2tm44ql.png)
CONCLUSION:
From the detailed explanation, we can see that the correct answer is:
![(-5,\text{ 4); r = 3 ( OPTION }C)](https://img.qammunity.org/2023/formulas/mathematics/college/x8cf9whdpoz65oya2wu8us715ogjb3i5tc.png)