Question

the equation of a circle is given below. identify the radius and the center. then graph the circle.
$x^2 + y^2 + 2x - 6y + 1 = 0$
radius:
center:
(there are also some input boxes and a coordinate plane with drawing tools in the image)

Explanation:

Step1: Group x and y terms

$x^2 + 2x + y^2 - 6y = -1$

Step2: Complete the square for x

$x^2 + 2x + 1 = (x+1)^2$, add 1 to both sides

Step3: Complete the square for y

$y^2 -6y +9 = (y-3)^2$, add 9 to both sides

Step4: Rewrite as circle equation

$(x+1)^2 + (y-3)^2 = (-1 +1 +9) = 9$

Step5: Identify center and radius

Center $(-1,3)$, radius $\sqrt{9}=3$

Answer:

Radius: 3
Center: (-1, 3)
(Graph: Plot center (-1,3) and draw a circle with radius 3 on the grid)