Eqution of circles: identify the center and radius of each?

I'll answer your question, but I'm going to give you a bit more info than you need, because by tomorrow you will be looking at problems slightly harder than this one.

If you had a term with just x, you would complete the square to find the x-coordinate of the center. E.g., if this were

x^2+ 4x + y^2= 29

Then you take 1/2 the coefficient of x, square it, and add it to both sides.

4/2 squared is 4, so this would become

x^2 + 4x + 4 + y^2 = 29 + 4 = 33

(x+2)^2 + y^2 = 33.

That would be a circle with center (-2, 0) and radius √33.

If you had a y term, you'd have to use that to complete the square to get (y-k)^2.

But your example is much easier, almost trivial. There is no x or y term so you don't have to complete any squares. These are already like (x-0)^2 + (y-0)^2 = 29, so just looking at it immediately tells you the center is (0,0).

After you complete the squares, the constant term left over is the square of the radius.

x² + y² = 29

(x)² + (y)² = 29

(x + 0)² + (y + 0)² = (√29)²

The typical equation of a circle is : (x - xo)² + (y - yo)² = R² → where

xo : abscissa of center → 0 in your case

yo : ordinate of center → 0 in your case

R : radius of circle → √29 in your case

The coordinates of the center of the circle are (0 ; 0) and the radius is √29