The equation \((x - 3)^2 + (y + 4)^2 = 25\) represents the equation of a circle in standard form.

### Standard form of a circle equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius.

### Solution:
- The center of the circle is \((h, k) = (3, -4)\).
- The radius \(r\) is \(\sqrt{25} = 5\).

Thus, the equation \((x - 3)^2 + (y + 4)^2 = 25\) describes a circle with:
- Center at \((3, -4)\).
- Radius \(5\).

Would you like more details on how this relates to graphing, or do you have any specific questions?

Here are 5 related questions:
1. How do you graph this circle on a coordinate plane?
2. What is the general form of a circle's equation?
3. How does changing the center of the circle affect its equation?
4. What happens to the equation if the radius changes?
5. Can you rewrite this circle's equation in a different form?

**Tip:** The square root of the constant on the right-hand side of the equation always gives the radius of the circle.

Understand how to analyze and solve the equation of a circle (x - 3)² + (y + 4)² = 25. This guide covers key geometric concepts, including identifying the center and radius of the circle. Perfect for students in Grades 8-10.

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