The given equation is:

\[
\frac{(x - 2)^2}{16} + \frac{(y - 1)^2}{25} = 1
\]

This is the equation of an **ellipse** in standard form. The standard form of an ellipse equation is:

\[
\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1
\]

where:
- \((h, k)\) is the center of the ellipse,
- \(a\) is the semi-major axis (along the x-axis if \(a > b\), or along the y-axis if \(b > a\)),
- \(b\) is the semi-minor axis.

### Breakdown:
- The center of the ellipse is \((h, k) = (2, 1)\).
- The value \(a^2 = 16\), so \(a = 4\).
- The value \(b^2 = 25\), so \(b = 5\).

Since \(b > a\), the semi-major axis is along the y-axis with length \(2b = 10\), and the semi-minor axis is along the x-axis with length \(2a = 8\).

### Conclusion:
- **Center**: \((2, 1)\)
- **Semi-major axis**: 5 (length = 10, along the y-axis)
- **Semi-minor axis**: 4 (length = 8, along the x-axis)

Do you want more details or have any questions?

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Here are five related questions you might consider:
1. How do you find the foci of this ellipse?
2. What is the eccentricity of this ellipse?
3. How would the equation change if the ellipse was rotated?
4. Can you write the parametric equations for this ellipse?
5. How do you find the area of the ellipse?

**Tip**: For ellipses, the larger the difference between \(a\) and \(b\), the more "stretched" the ellipse becomes.

(𝑥 − 2)^2 / 16 + (𝑦 − 1)^2 / 25 = 1

Explore how to solve the ellipse equation (x - 2)^2 / 16 + (y - 1)^2 / 25 = 1. Learn key concepts, including identifying the center, semi-major and semi-minor axes, and the properties of ellipses. Suitable for high school students in Grades 9-12.

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