Write the standard form of the equation and the general form of the equation of the circle with radius r and center​ (h,k). Then graph the circle.
requals5​;    ​(h,k)equalsleft parenthesis negative 2 comma 1 right parenthesis

The graph above shows the circle with a center at \((-2, 1)\) and a radius of 5. The circle is plotted according to the standard form equation:

\[
(x + 2)^2 + (y - 1)^2 = 25
\]

with its center marked in red.

### Summary:
- **Standard Form**: \((x + 2)^2 + (y - 1)^2 = 25\)
- **General Form**: \(x^2 + y^2 + 4x - 2y - 20 = 0\)

Would you like further details or have any questions? Here are some related questions you might be interested in:

1. How to find the equation of a tangent line to a circle?
2. What is the relationship between the general and standard forms of a circle's equation?
3. How to determine if a point lies inside, on, or outside a circle?
4. How to derive the equation of a circle given three points?
5. What is the parametric form of a circle's equation?

**Tip:** Understanding how to convert between the standard and general forms of a circle's equation can help in solving more complex geometry problems involving circles!

Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle. r equals 5; (h,k) equals (-2, 1).

Explore how to find the standard and general forms of the equation of a circle with a center at (-2, 1) and a radius of 5. Learn key geometry concepts, including equations of circles, and see a graph of the circle. Suitable for Grades 9-10.

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