https://file.aiquickdraw.com/mathbot/file/1727031774731ocmfok6z.jpg

The equation of the circle provided is:

\[
x^2 + (y - 2)^2 = 16
\]

This equation follows the standard form of a circle's equation:

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

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

### Step 1: Identify the Center
From the equation, we can see that the center \((h, k)\) is \((0, 2)\), because:
- For \(x^2\), the center along the x-axis is \(0\).
- For \((y - 2)^2\), the center along the y-axis is \(2\).

Thus, the center is \((0, 2)\).

### Step 2: Identify the Radius
The right-hand side of the equation is \(16\), which corresponds to \(r^2\). Therefore, the radius is the square root of \(16\), which is \(r = 4\).

### Summary:
- Radius: \(4\)
- Center: \((0, 2)\)

### Graphing the Circle:
- The center is at the point \((0, 2)\).
- The circle has a radius of 4, so the points on the circle will be 4 units away from the center in all directions.

Would you like me to provide more details, such as steps to graph the circle manually?

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Here are five related questions to further explore this topic:
1. How can you derive the equation of a circle if the center and radius are known?
2. What is the relationship between the radius and the area of a circle?
3. How do you graph a circle when the center is not at the origin?
4. What happens to the equation of the circle if the radius is doubled?
5. How can the distance formula be used to verify if a point lies on the circle?

**Tip**: When graphing a circle, always start by plotting the center and then move \(r\) units in each direction (up, down, left, right) to draw the boundary of the circle.

Identify the radius and center of the circle from the equation x^2 + (y - 2)^2 = 16. Then graph the circle.

Learn how to find the radius and center of a circle from the equation x^2 + (y - 2)^2 = 16. Understand key concepts such as the standard form of a circle and how to graph it. Suitable for students in Grades 9-10.

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