Find the center and radius of each circle x^2+y^2-6x+2y+9=0

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

To obtain this form use the method of completing the square on both the x and y terms

x² - 6x + y² + 2y = - 9 ← rearranging

x² + 2(- 3)x + 9 + y² + 2(1)y + 1 = - 9 + 9 + 1

(x - 3)² + (y + 1)² = 1 ← in standard form

with centre (3, - 1) and radius 1