Answer :
We know that the equation of a circle is:
[tex](x-a)^2+(y-b)^2=R^2[/tex]
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
[tex](x-a)^2+(y-b)^2=R^2[/tex]
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).
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).