https://file.aiquickdraw.com/mathbot/file/1726072454186jcyeosux.jpg

To determine the equation of the circle from the graph, we need to identify two key elements:

1. **Center of the circle**: From the graph, the center is located at the origin, \((0, 0)\).
2. **Radius of the circle**: The circle touches the x-axis at \(x = 5\), so the radius is 5 units.

The general form of the equation of a circle is:

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

Where:
- \((h, k)\) is the center of the circle,
- \(r\) is the radius.

For this circle:
- \(h = 0\), \(k = 0\) (center is at the origin),
- \(r = 5\) (radius is 5 units).

Thus, the equation of the circle is:

\[
x^2 + y^2 = 5^2
\]
\[
x^2 + y^2 = 25
\]

This is the equation of the circle in the graph.

Would you like more details on this? Here are five related questions to explore this topic further:

1. What if the center of the circle was not at the origin?
2. How would the equation change if the radius was different?
3. Can you explain how to derive the general form of the circle equation?
4. What is the standard form of a circle equation, and how is it different from the general form?
5. How would you find the radius if only the equation of the circle was given?

**Tip**: When graphing or analyzing circles, always check the coordinates of the center and the radius from a key point on the circle!

Determine the equation of the circle graphed below.

Learn how to determine the equation of a circle centered at the origin with a radius of 5 units. This example demonstrates key geometry concepts, including circle equations and radius identification. Suitable for students in Grades 9-10.

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