Answer:
the center is (3,1) and the radius is √6.
Step-by-step explanation:
The center of a circle can be found using the equation [tex](x-h)^2 + (y-k)^2 = r^2[/tex] and is (h,k) from it. Notice h and k are the opposite value as in the equation.
First write the equation in this form.
[tex]x^2 - 6x + ( ?)+ y^2 - 2y + (?) + 4 = 0[/tex]
Complete the square with each variable to find what numbers should go in place of the question marks.
[tex](-6/2)^2 = -3^2 = 9[/tex]
[tex](-2/2)^2 = -1^2 = 1[/tex]
Add 1 and 9 to both sides of the equation.
[tex]x^2 - 6x + 9 + y^2 - 2y + 1 + 4 = 1 + 9\\(x-3)^2 + (y-1)^2 + 4 = 10\\(x-3)^2 + (y-1)^2 = 6[/tex]
So the center is (3,1) and the radius is √6.
