The general form of the equation of a circle is x2+y2+2x−6y+1=0.

What are the coordinates of the center of the circle?

Enter your answer in the boxes.

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