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:

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

Would you like a detailed explanation, the image of the graph, or both?

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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.