To graph the equation \( x^2 + y^2 = 72 \), follow these steps:

### 1. Recognize the Equation Type
The given equation \( x^2 + y^2 = 72 \) represents a circle centered at the origin (0, 0) with a radius \( r \).

### 2. Determine the Radius
The general form of a circle's equation is \( x^2 + y^2 = r^2 \). Here, \( r^2 = 72 \). 
To find the radius \( r \):

\[
r = \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \approx 8.49
\]

### 3. Plot the Circle
- **Center**: The center of the circle is at (0, 0).
- **Radius**: The radius is approximately 8.49 units.
  
To graph the circle:
- Plot the center at (0, 0).
- Mark points 8.49 units away from the center in all directions (up, down, left, and right).
- Draw a smooth curve that passes through these points to form a circle.

### 4. Graph Representation
The circle will touch the points approximately at (±8.49, 0) and (0, ±8.49) on the Cartesian plane.

Would you like to see a detailed step-by-step graphical representation of this process, or do you have any specific questions?

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**Relative Questions:**
1. What are the coordinates of points where the circle intersects the x-axis and y-axis?
2. How would the graph change if the equation were \( x^2 + y^2 = 100 \)?
3. Can you graph the equation \( (x - 2)^2 + (y + 3)^2 = 25 \)?
4. What is the significance of the radius in the graph of a circle?
5. How would you determine if a point lies inside, on, or outside the circle?

**Tip:** The radius of a circle from its equation \( x^2 + y^2 = r^2 \) is always \( \sqrt{r^2} \), which helps determine the size and scale of the graph.

Learn how to graph the circle given by the equation x^2 + y^2 = 72 with this detailed step-by-step guide. Understand the concept of circles in geometry and how to plot them on a Cartesian plane. Suitable for students in Grades 7-9.

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