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!