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Answer:
The answer to your question is Center: (-1 , 3)
Step-by-step explanation:
Data
x² + y² + 2x - 6y + 1 = 0
Process
1.- Group like terms pass the independent term to the right side
(x² + 2x ) + (y² - 6y ) = -1
2.- Divide the second term of each group by 2 and write the result in the third position of each group to the second power. Write these numbers also in the right side of the equation.
(x² + 2x + (1)²) + (y² - 6y + (3)²) = -1 + (1)² + (3)²
3.- Factor in the left side and simplify in the right side
(x + 1)² + (y - 3)² = -1 + 1 + 9
4.- Simplify
(x + 1)² + (y - 3)² = 9
5.- Find the center and the radius
Center: (-1 , 3)
radius = = 3