1. **State the problem:** We are given the ellipse equation $$\frac{(x + 11)^2}{25} + \frac{(y - 2)^2}{9} = 1$$ and need to analyze its properties. 2. **Formula and rules:** The standard form of an ellipse centered at $ (h, k) $ is: $$\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$$ where $a$ and $b$ are the lengths of the semi-major and semi-minor axes respectively. 3. **Identify center and axes:** From the equation, center is $(-11, 2)$. Denominators give $a^2 = 25$ and $b^2 = 9$. So, $a = 5$ and $b = 3$. 4. **Determine major and minor axes:** Since $a > b$, the major axis length is $2a = 10$ and minor axis length is $2b = 6$. 5. **Find foci:** Foci distance from center is $c = \sqrt{a^2 - b^2} = \sqrt{25 - 9} = \sqrt{16} = 4$. Since major axis is along x-axis, foci are at $(-11 \pm 4, 2)$, i.e., $(-15, 2)$ and $(-7, 2)$. 6. **Summary:** - Center: $(-11, 2)$ - Semi-major axis: $5$ - Semi-minor axis: $3$ - Foci: $(-15, 2)$ and $(-7, 2)$ **Final answer:** The ellipse is centered at $(-11, 2)$ with semi-major axis length $5$ along the x-axis and semi-minor axis length $3$ along the y-axis.