+9481 Let's get the equation into the form
(x - h)2 + (y - k)2 = r2 where the point (h, k) is the center of the circle and r is the radius.
9x2 - 18x + 9y2 + 36y + 44 = 0
Subtract 44 from both sides of the equation
9x2 - 18x + 9y2 + 36y = -44
Divide both sides by 9
x2 - 2x + y2 + 4y = - \(\frac{44}{9}\)
Add 1 and add 4 to both sides to complete the squares on the left side
x2 - 2x + 1 + y2 + 4y + 4 = - \(\frac{44}{9}\) + 1 + 4
Factor both perfect square trinomials on the left side
(x - 1)2 + (y + 2)2 = - \(\frac{44}{9}\) + 1 + 4
Get a common denominator to combine - \(\frac{44}{9}\) + 1 + 4
(x - 1)2 + (y + 2)2 = - \(\frac{44}{9}\) + \(\frac99\) + \(\frac{36}{9}\)
(x - 1)2 + (y + 2)2 = \(\frac19\)
Now it is in the form (x - h)2 + (y - k)2 = r2 and we can see that...
r2 = \(\frac19\)
The radius is positive so take the positive sqrt of both sides
r = \(\frac13\)
