https://file.aiquickdraw.com/mathbot/file/1727708186249r5w0ge5s.jpg

The diagram shows an ellipse centered at the origin (0, 0), with the x-axis representing the major axis (length of 30) and the y-axis representing the minor axis (length of 18).

In general, the standard form of an ellipse's equation is:

\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]

where:
- \(a\) is the semi-major axis (half the length of the major axis),
- \(b\) is the semi-minor axis (half the length of the minor axis).

From the diagram:
- The total length of the major axis is 30, so \(a = \frac{30}{2} = 15\).
- The total length of the minor axis is 18, so \(b = \frac{18}{2} = 9\).

Thus, the equation of the ellipse is:

\[
\frac{x^2}{15^2} + \frac{y^2}{9^2} = 1
\]
\[
\frac{x^2}{225} + \frac{y^2}{81} = 1
\]

Now, checking the options:
- Option B matches this equation exactly.

Therefore, the correct answer is **B**.

Would you like more details or have any questions?

Here are five related questions:
1. How do we calculate the foci of an ellipse?
2. What is the relationship between the major and minor axes in an ellipse?
3. How do you find the eccentricity of an ellipse?
4. How do we derive the equation for ellipses that aren't centered at the origin?
5. How can ellipses be used to model planetary orbits in space?

**Tip:** In an ellipse, the sum of the distances from any point on the ellipse to the two foci is always constant!

The accompanying diagram shows the construction of a model of an elliptical orbit of a planet traveling around a star. Point P and the center of the star represent the foci of the orbit. Which equation could represent the relation shown?

Learn how to determine the equation of an ellipse representing a planet's elliptical orbit around a star. This problem involves calculating the semi-major and semi-minor axes from the diagram and identifying the correct equation of the ellipse. Suitable for Grades 9-12.

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