Find the equation of the circle with center (3,-2) and radius 2 units.

The general equation of a circle is given by:

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

Where:
- \((h, k)\) is the center of the circle,
- \(r\) is the radius.

Given:
- Center: \((3, -2)\),
- Radius: \(2\) units.

Substituting the values into the equation:

\[
(x - 3)^2 + (y + 2)^2 = 2^2
\]

Simplifying:

\[
(x - 3)^2 + (y + 2)^2 = 4
\]

Thus, the equation of the circle is:

\[
(x - 3)^2 + (y + 2)^2 = 4
\]

Would you like more details or further clarification?

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Here are 5 related questions for further exploration:
1. How would the equation change if the radius was doubled?
2. What is the equation of a circle with a center at the origin and a radius of 5?
3. How can you find the diameter of the circle given its equation?
4. How do you determine if a point lies inside, on, or outside the circle?
5. Can you rewrite the equation in a different form, such as expanded form?

**Tip:** To find whether a point lies inside a circle, calculate the distance from the point to the center and compare it with the radius.

Learn how to find the equation of a circle with a center at (3, -2) and a radius of 2 units. This problem involves key geometric concepts like the standard equation of a circle and is suitable for students in Grades 9-10.

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