Question

A circle is defined by the equation: x^2 + y^2 – x – 2y – 11/4 = 0. Determine the coordinates for the center of the circle and the length of the radius.

Answer 1

x^2 + y^2 – x – 2y – 11/4 = 0
x^2 - x + y^2 - 2y = 11/4

Using completing the square method:

x^2 - x + 1/4 + y^2 - 2y + 1 = 11/4 + 1 + 1/4
(x - 1/2)^2 + (y - 1)^2 = 4

coordinates: (1/2 , 1)
radius: sqrt (4)