Question

the equation of a circle is given below. identify the radius and the center. then graph the circle.
$x^2 + y^2 - 2x - 6y + 6 = 0$
radius:
center: ( , )

Explanation:

Step1: Rearrange the equation

Group x and y terms: $(x^2 - 2x) + (y^2 - 6y) = -6$

Step2: Complete the square for x

$x^2 - 2x = (x-1)^2 - 1$

Step3: Complete the square for y

$y^2 - 6y = (y-3)^2 - 9$

Step4: Substitute back and simplify

$(x-1)^2 -1 + (y-3)^2 -9 = -6$ → $(x-1)^2 + (y-3)^2 = 4$

Step5: Identify center and radius

Standard form: $(x-h)^2 + (y-k)^2 = r^2$ → center $(h,k)=(1,3)$, $r^2=4$ → $r=2$

Answer:

Radius: 2
Center: (1, 3)
(Graph: Plot center (1,3), draw circle with radius 2 units)