Question

A circle is defined by the equation x2 + y2 – x – 2y – = 0. What are the coordinates for the center of the circle and the length of the radius?

Answer 1

x^2 + y^2 - x - 2*y = 0
To find both coordinates and radius we need to make this equation in circle form:
(x-a)^2 + (y-b)^2 = r^2

x^2 - 2*1/2*x + 1/4 - 1/4 + y^2 - 2*1*y + 1 - 1 = 0
Here we are adding and subtracting numbers in order to get square binomial.
(x - 1/2)^2 + (y-1)^2 = 5/4

coordinates of center are (1/2,1) and the radius is √$\frac{5}{4}$

Answer 2

  x2 + y2 – x – 2y – = 0. 
x2  – x  +y2– 2y – = 0. 
(x2  – x +1/4) +(y2– 2y+1) =1/4 +1
(x-1/2)^2+(y-1)^2=1/2+5/2
(x-1/2)^2+(y-1)^2=3/2
center (1/2,1)
radiusSqrt 3/2