To graph the equation \( x^2 + y^2 = 72 \), we need to recognize that this equation represents a circle in the coordinate plane.

### Steps to Graph:
1. **Identify the form of the equation**: The given equation is in the standard form of a circle, \( x^2 + y^2 = r^2 \), where \( r \) is the radius of the circle.
   
2. **Calculate the radius**: 
   \[
   r = \sqrt{72} \approx 8.49
   \]

3. **Plot the center**: The circle is centered at the origin \((0, 0)\).

4. **Plot the radius**: From the origin, you would draw a circle with a radius of approximately 8.49 units.

### Graph Details:
- **Center**: \((0, 0)\)
- **Radius**: \( \sqrt{72} \approx 8.49 \)

Here is the visual representation:

\[
\text{Circle with center } (0, 0) \text{ and radius } 8.49.
\]

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### Relative Questions:
1. What is the general equation of a circle in the coordinate plane?
2. How do you determine the radius and center from the equation of a circle?
3. How does changing the radius affect the graph of a circle?
4. What happens if the equation was \(x^2 + y^2 = r^2 + c\), where \(c\) is a constant?
5. How would the graph change if the circle were shifted from the origin?

**Tip:** When graphing circles, always check if the equation is in standard form. If not, complete the square to find the center and radius.

Learn how to graph the circle equation x² + y² = 72 with a step-by-step guide. This problem covers key concepts in coordinate geometry, including circle equations and plotting coordinates. Suitable for high school students.

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