The given equation of the circle is:

$(x+2)^2 + (y-1)^2 = 9$

This equation is in the standard form of a circle, which is:

$(x - h)^2 + (y - k)^2 = r^2$

where:

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

Step 1: Identify the center and radius

• From the given equation $(x + 2)^2 + (y - 1)^2 = 9$, we can compare it to the standard form.
  • The center $(h, k)$ is $(-2, 1)$, because $(x + 2)$ can be rewritten as $(x - (-2))$, and $(y - 1)$ matches the $(y - k)$ form.
  • The radius $r$ is the square root of 9, which is $r = 3$.

Conclusion:

• Center: $(-2, 1)$
• Radius: $3$

Step 2: Graph the Circle

To graph the circle, plot the center $(-2, 1)$ on a coordinate plane. Then, from the center, move 3 units in all directions (up, down, left, right) to mark points on the circle. You can sketch the circle by connecting these points smoothly.

Would you like me to generate a graph of the circle for you?

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If you have any further questions or need more details, feel free to ask!

Here are some related questions to explore:

1. How do you derive the standard form of a circle from the general equation of a circle?
2. How can you convert from general form to standard form for circles?
3. What are the differences between an equation of a circle and the equation of other conic sections, like ellipses or hyperbolas?
4. How do you calculate the area and circumference of a circle from its radius?
5. What happens if the right-hand side of the equation changes (e.g., $=16$ instead of $=9$)?

Tip: When graphing a circle, make sure to remember that the radius is the distance from the center to any point on the circle.