https://r2.erweima.ai/mathbot/image/1726636534676dngyw9z8.jpg

The image shows a circle on a coordinate plane, along with the request to determine the **ordinary equation of the circle** based on the information from the graph.

### Key observations from the graph:
1. **Center of the circle (C)**: The center of the circle appears to be at the origin \( (0, 0) \), as the circle is symmetrically placed around the origin.
2. **Radius (r)**: From the graph, we can estimate the radius by observing the distance from the center to any point on the circle. For instance, the point \( P \) on the circle seems to be at \( (5, 0) \), which indicates that the radius \( r = 5 \).

### Equation of the circle:
The general equation of a circle with center \( (h, k) \) and radius \( r \) is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Since the center is \( (0, 0) \) and the radius is \( 5 \), the equation simplifies to:

\[
x^2 + y^2 = 5^2
\]

\[
x^2 + y^2 = 25
\]

### Final Answer:
The equation of the circle is:
\[
x^2 + y^2 = 25
\]

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### Related Questions:
1. How do you find the center and radius of a circle from its equation?
2. What is the geometric meaning of the equation \( x^2 + y^2 = r^2 \)?
3. How would the equation change if the circle's center were at \( (h, k) \) instead of the origin?
4. Can you describe how to derive the equation of a circle from general points on the circumference?
5. How do translations affect the equation of a circle?

**Tip:** When working with graphs, always try to identify key features like the center and radius directly from the diagram to write the equation quickly.

Determine the ordinary equation of the circle based on the information from its graph.

Learn how to derive the equation of a circle based on the center and radius from a given graph. This problem covers concepts in analytic geometry, including the standard form equation of a circle.

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