Acircle is defined by the equation given below.
x^2 + y^2 − x − 2y − 11/4 = 0
what are the coordinates for the center of the circle and the length of the radius?

We know that the equation of a circle is:



where a and b are the coordinates of the center, and R is the radius.

So in this question we have to complete the squares:

x² + y² - x - 2y - 11/4 = 0       ----->
x² - x + 1/4 + y² - 2y = 11/4 +1/4     ------->
(x - 1/2)² + y² - 2y + 1 = 12/4 + 1     ----->
(x - 1/2)² + (y - 1)² = 4

Therefore, the coordinates of the center are C = ( 1/2 , 1) and the Radius is R = 2

       x² + y² - x - 2y - 2³/₄ = 0
                x² + y² - x - 2y = 2³/₄
                x² - x + y² - 2y = 2³/₄
(x² - x + 1) + (y² - 2y + 4) = 2³/₄ + 1 + 4
              (x - 1)² + (y - 2)² = 7³/₄

The coordinates for center of the circle is equal to (1, 2). The coordinates of the length of the radius is √(³¹/₄).