X^2+y^2 - 2y - 99 = 0

What is the center of this circle? What is the radius of this circle

Center: (0, 1); radius: 10

Step-by-step explanation:

Your x^2+y^2 - 2y - 99 = 0 is centered at (0, k):

(x - 0) ^2 + y^2 - 2y - 99 = 0

and you must "complete the square" of y^2 - 2y

to determine the value of k:

(x - 0) ^2 + y^2 - 2y + 1 - 1 - 99 = 0, or

(x - 0) ^2 + (y - 1) ^2 = 100 = 10^2

The center is at (h, k) : (0, - 1) and the radius is 10.

The equation in final form is

x^2 + (y - 1) ^2 = 10^2

The radius is 10. That is, since r^2 = 100, r must be 10.