Please help! A circle is defined by the equation 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?

Step-by-step explanation:

We know that the equation of a circle is:

(

x

−

a

)

2

+

(

y

−

b

)

2

=

R

2

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).

18.75 gallons

step-by-step explanation: