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The given equation models the moon's orbit and is in the form:

\[
\frac{x^2}{63,500} + \frac{y^2}{50,900} = 1
\]

This is the equation of an ellipse, where the denominators are the squares of the semi-major and semi-minor axes (denoted as \(a\) and \(b\), respectively).

1. The semi-major axis \(a\) is the square root of 63,500:
   \[
   a = \sqrt{63,500} \approx 252.0 \text{ thousand miles} = 252,000 \text{ miles}
   \]

2. The semi-minor axis \(b\) is the square root of 50,900:
   \[
   b = \sqrt{50,900} \approx 225.6 \text{ thousand miles} = 225,600 \text{ miles}
   \]

The distance closest to the center of the orbit corresponds to the value of the semi-minor axis, which is 225,600 miles.

Thus, the correct answer is indeed **225,600 miles**.

Would you like a detailed explanation of how ellipses model orbits, or do you have any other questions?

### Related Questions:
1. What is the general form of an ellipse equation?
2. How do we determine the distance between foci in an elliptical orbit?
3. How do we interpret the semi-major and semi-minor axes physically in an orbit?
4. How does the moon's orbit deviate from a perfect circle?
5. How is eccentricity of an orbit calculated from the ellipse parameters?

### Tip:
In an elliptical orbit, the semi-major axis represents the average distance from the center to the orbiting body, while the semi-minor axis represents the closest approach distance.

If the orbit of the moon can be modeled using the equation x^2/63,500 + y^2/50,900 = 1, what is the closest that the moon travels to the center of its orbit?

Find the closest distance the moon travels to the center of its elliptical orbit using the equation x^2/63,500 + y^2/50,900 = 1. This problem involves key concepts from conic sections, including calculating semi-major and semi-minor axes of an ellipse. Suitable for high school students in Grades 9-12.

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