https://file.aiquickdraw.com/mathbot/file/1727025831473h1v0veb5.jpg

To find the equation of the circle, we need the following pieces of information from the graph:

1. **Center of the circle (h, k)**: The center can be identified as the point around which the circle is symmetric.
2. **Radius (r)**: This is the distance from the center to any point on the circle.

From the image:
- The center of the circle appears to be at \((6, 0)\).
- The radius can be observed as the distance from the center \((6, 0)\) to the point where the circle crosses the x-axis at \(x = 9\), so the radius \(r = 3\).

The general equation of a circle in **center-radius form** is:

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

Substituting the values \(h = 6\), \(k = 0\), and \(r = 3\):

\[
(x - 6)^2 + y^2 = 9
\]

So, the equation of the circle is:

\[
(x - 6)^2 + y^2 = 9
\]

Would you like more details or have any other questions?

Here are 5 related questions you can explore:
1. How do we derive the center-radius form of a circle's equation?
2. What is the relationship between the general form and the center-radius form of a circle's equation?
3. How can we find the radius from the diameter or the circumference?
4. Can this equation be converted into the general form of a circle equation?
5. How can you determine the equation of a circle given three points on the circle?

**Tip**: Always double-check the coordinates of the center and the radius by counting grid squares carefully to ensure accuracy in reading the graph!

Find the equation of the circle shown. Write the equation in center-radius (or standard) form.

Learn how to find the equation of a circle from a graph. This problem explores identifying the center and radius of a circle and writing the equation in center-radius form. Suitable for students in Grades 8-10.

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