# How Do You Find the Domain and Range of a Circle?

The domain of a circle is the X coordinate of the center of the circle plus and minus the radius of the circle. The range of a circle is the Y coordinate of the center of the circle plus and minus the radius of the circle. It is easy to remember which coordinates domain and range refer to because X is alphabetically before Y, and domain is alphabetically before range.

The standard form of the formula for a circle is (x -a )^2 + (y – b)^2 = r^2, where “a” is the X coordinate of the center of the circle, “b” is the Y coordinate of the center of the circle and “r” is the radius of the circle. Therefore, the center of the circle has coordinates (a,b), and the radius is the square root of the number to the right of the equal sign. The formula for the domain of a circle is {x| a – r < x < a + r}. The formula for the range of a circle is {y| b - r < y < b + r}.

The domain gives the maximum and minimum values for the X coordinates of the circle, while the range gives the maximum and minimum values for the Y coordinates of the circle. All values of points on the circle fall within the domain and range of the circle.