https://file.aiquickdraw.com/mathbot/file/1725422477754yux7yvib.jpg

To find the equation of the circle in the given image, we need to determine the center \((h, k)\) and the radius \(r\) of the circle.

### Analyzing the Image:

1. **Identify the center of the circle:**  
   From the graph, it appears that the circle is centered at the point \((1, 0)\).

2. **Determine the radius of the circle:**  
   The circle seems to pass through the point \((0, 0)\), which is one unit away from the center. Thus, the radius \(r = 1\).

### Equation of a Circle:

The standard equation for a circle with center \((h, k)\) and radius \(r\) is given by:

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

### Substituting the Center and Radius:

- Center: \((h, k) = (1, 0)\)
- Radius: \(r = 1\)

\[
(x - 1)^2 + (y - 0)^2 = 1^2
\]

### Simplified Equation:

\[
(x - 1)^2 + y^2 = 1
\]

### Conclusion:

The equation for the circle is:

\[
(x - 1)^2 + y^2 = 1
\]

Would you like more details or have any questions?

### Related Questions:

1. What is the general form of the equation of a circle?
2. How do you convert the equation of a circle from standard form to general form?
3. How can you determine the radius of a circle given its equation in standard form?
4. How do you find the center of a circle if the equation is given in general form?
5. How does the graph change if the circle's radius is doubled?

### Tip:

When identifying the center and radius of a circle from a graph, look for points that are equidistant from the center to help determine the radius accurately.

Learn how to determine the equation of a circle by identifying its center and radius from a graph. This example involves finding the center at (1, 0) and the radius of 1, then using the circle equation formula. Perfect for students in Grades 9-11.

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