We are given the equation of a circle:

$x^2 + y^2 = 9$

Step 1: Recall the general form of the equation of a circle

The standard form of the equation of a circle is: $(x-h)^2 + (y-k)^2 = r^2$ Where:

• $(h, k)$ is the center of the circle.
• $r$ is the radius.

Step 2: Compare the given equation with the standard form

The given equation is: $x^2 + y^2 = 9$

• Since there are no $(x-h)$ or $(y-k)$ terms, the center is at $(0, 0)$.
• The right-hand side of the equation, $9$, represents $r^2$. So, $r = \sqrt{9} = 3$.

Final Answer:

• Center: $(0, 0)$
• Radius: $3$

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Step 3: Graph the circle

To graph the circle:

1. Plot the center at $(0, 0)$.
2. Draw a circle with radius $3$, meaning the circle passes through points:
   • $(3, 0)$, $(-3, 0)$, $(0, 3)$, and $(0, -3)$.

Would you like me to generate an image of this graph or explain further?

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5 Related Questions:

1. What is the equation of a circle with a center at $(2, -1)$ and radius $5$?
2. How do you determine the radius from a circle's equation?
3. What changes in the equation if the center is not at the origin?
4. How can you graph a circle given its equation in standard form?
5. Can a circle have a radius of $0$? If so, what does it represent?

Tip: Always check if the circle's equation is in standard form to identify the center and radius easily!