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The problem asks for the equation of a circle given the following conditions:

- The center of the circle is \( (2, -1) \).
- The radius of the circle is \( 2 \).

The general equation for a circle with center \( (h, k) \) and radius \( r \) is given by:

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

Here, the center is \( (2, -1) \) and the radius is \( 2 \). Substituting these values into the equation:

\[
(x - 2)^2 + (y + 1)^2 = 2^2
\]

Simplifying:

\[
(x - 2)^2 + (y + 1)^2 = 4
\]

So, the equation of the circle is:

\[
(x - 2)^2 + (y + 1)^2 = 4
\]

Let me know if you want more details or have any questions!

Here are some related questions to explore this topic further:
1. What is the equation of a circle with center at \( (-3, 5) \) and radius \( 7 \)?
2. How do you determine the radius from a given circle equation?
3. How do you find the center of a circle from its equation?
4. What is the standard form of a circle's equation, and how does it differ from the general form?
5. How can you graph a circle from its equation?

**Tip:** To quickly find the radius from a circle's equation, take the square root of the number on the right side of the equation!

Find an equation of the circle that satisfies the given conditions: Center (2, -1), radius 2.

Learn how to find the equation of a circle with a center at (2, -1) and a radius of 2. This problem explores key geometric concepts and the formula for a circle's equation. Suitable for students in Grades 9-12.

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