The given equation is:

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

This is the equation of a circle in standard form:

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

Where:

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

By comparing the given equation with the standard form:

• The center $(h, k)$ is $(-1, 2)$.
• The radius $r$ is $\sqrt{9} = 3$.

Summary:

• Center: $(-1, 2)$
• Radius: $3$

Would you like further details on how this was derived, or have any other questions?

Here are 5 related questions:

1. How do you convert a general circle equation to standard form?
2. What are the characteristics of a circle with a center at the origin?
3. How can you graph a circle given its equation?
4. What happens if the equation of a circle is expanded, and how can you simplify it?
5. How do you find the equation of a circle if you know the center and a point on the circle?

Tip: To identify the center and radius quickly, rewrite the equation in standard form and compare it directly with $(x - h)^2 + (y - k)^2 = r^2$.