Step-by-step Solution:

Explanation:

We are given the circle equation: \[ x^{2} + y^{2} + 6x - 4y + 4 = 0 \]

Step 1: Rearrange terms

\[ x^{2} + 6x + y^{2} - 4y + 4 = 0 \]

Step 2: Complete the squares

\[ (x^{2} + 6x + 9) + (y^{2} - 4y + 4) = -4 + 9 + 4 \] \[ (x+3)^{2} + (y-2)^{2} = 9 \]

Step 3: Identify center and radius

• Center = \((-3, 2)\)
• Radius = \(\sqrt{9} = 3\)

✅ Correct option is: (D) (-3, 2) and 3