Question

the equation of a circle is given below. identify the center and the radius. then graph the circle.
$x^2 + y^2 + 6x + 2y - 15 = 0$
center: ( , )
radius:
graph of a coordinate plane with x-axis from -8 to 6 and y-axis from -8 to 8, grid lines present

Explanation:

Step1: Group x and y terms

$x^2 + 6x + y^2 + 2y = 15$

Step2: Complete the square for x

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

Step3: Complete the square for y

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

Step4: Rewrite as standard form

$(x+3)^2 + (y+1)^2 = 15 +9 +1 =25$

Step5: Identify center and radius

Standard form: $(x-h)^2 + (y-k)^2 = r^2$, so $h=-3,k=-1,r=5$

Answer:

Center: (-3, -1)
Radius: 5
(Graph: Plot center (-3,-1), draw circle with radius 5 on the grid)