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The equation given is:

\[
\frac{x^2}{9} + \frac{y^2}{25} = 1
\]

This represents the equation of an ellipse in standard form:

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

Here, \(a^2 = 9\), so \(a = 3\), and \(b^2 = 25\), so \(b = 5\). 

- The center of the ellipse is at \((0, 0)\), since the equation is not shifted horizontally or vertically.
- The semi-major axis is along the y-axis (since 25 > 9), and its length is \(5\).
- The semi-minor axis is along the x-axis, and its length is \(3\).

The vertices of the ellipse occur along the axes. Therefore:
- The vertices along the x-axis are \((\pm 3, 0)\).
- The vertices along the y-axis are \((0, \pm 5)\).

Thus, the vertices are \((0, 5)\) and \((0, -5)\), which corresponds to the correct answer: **"0, 5 and 0, -5"**.

Would you like further details or have any questions? 

Here are 5 related questions:
1. How do you determine the center of an ellipse?
2. What is the significance of the semi-major and semi-minor axes?
3. How can you identify the shape of a conic from its equation?
4. How are ellipses related to hyperbolas and circles in conic sections?
5. What is the formula for the eccentricity of an ellipse?

**Tip**: Always check if the denominator under \(x^2\) or \(y^2\) is larger to determine the orientation of the ellipse.

What is the vertex (are the vertices) of the shape defined by the equation (x^2 / 9) + (y^2 / 25) = 1?

Learn how to determine the vertices of an ellipse using the equation (x^2 / 9) + (y^2 / 25) = 1. This problem covers concepts like the semi-major axis, semi-minor axis, and identifying conic sections, suitable for high school geometry students.

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