The Cartesian Circle
Written by tutor Steve C.
There are three locations for graphing a circle in the XY Cartesian Plane:
At the Origin, On the Edge, and Anyplace Else.
Here is the standard circle with center at the origin, defined by x^{2} + y^{2} = 16
The general form is actually x^{2} + y^{2} = r^{2} where the radius r = 4
Here is the same size circle with center at (5, 5), defined by (x5)^{2} + (y5)^{2} = 16
The general form is actually
(xa)^{2} + (yb)^{2} = r^{2} where the center is (a, b). Notice that the center points here are 
If the circle center is at (5, 5)
then the standard form of the circle becomes (x+5)^{2} + (y+5)^{2} = 16 A similar pattern will result if the 
The Special Case
The final location for a circle graph is where the edge falls along the x axis and y axis.
Here is the same size circle with center at (4, 4), defined by (x4)^{2} + (y4)^{2} = 16.
The standard form of the equation is still (xa)^{2} + (yb)^{2} = r^{2} .
However, in this case, a = b = r. In fact, we can state that the graph of the equation in this form (xr)^{2} + (yr)^{2} = r^{2} Is a circle sitting on the edge of the x axis and the y axis. 
We can carry this further, (for the 1st quadrant only) where (xa)^{2} + (yb)^{2} = r^{2} : if a=r, the circle sits on the x axis; if b=r, the circle sits on the y axis; 

(x2)^{2} + (y4)^{2} = 4^{2} (x4)^{2} + (y2)^{2} = 4^{2} 