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Let's analyze and solve the given equations to find the requested properties.

### Problem 4:  
**Equation:**  
\[
x^2 + y^2 - 6x + 2y + 9 = 0
\]

1. **Complete the square** for \( x \)- and \( y \)-terms to convert the equation into standard form:

\[
(x^2 - 6x) + (y^2 + 2y) = -9
\]

Completing the square:
\[
(x - 3)^2 - 9 + (y + 1)^2

4. x^2 + y^2 - 6x + 2y + 9 = 0; 5. x^2 + y^2 + 4x + 2y - 20 = 0

Learn how to solve circle equations such as x^2 + y^2 - 6x + 2y + 9 = 0 and x^2 + y^2 + 4x + 2y - 20 = 0 by completing the square. This guide covers the center and radius calculations and graphing techniques, ideal for Grades 9-11 students studying conic sections.

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