Identify the center and radius of (𝑥 + 1)
2 + (𝑦 − 2)
2 = 9

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

Identify the center and radius of (𝑥 + 1)^2 + (𝑦 − 2)^2 = 9

Learn how to identify the center and radius of a circle from the equation (x + 1)^2 + (y − 2)^2 = 9. This problem covers the standard form of a circle equation, suitable for students in Grades 9-10.

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