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 x2 + y2 = 16
The general form is actually x2 + y2 = r2 where the radius r = 4
Here is the same size circle with center at (5, 5), defined by (x-5)2 + (y-5)2 = 16
|The general form is actually
(x-a)2 + (y-b)2 = r2
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 (x-4)2 + (y-4)2 = 16.
|The standard form of the equation is still (x-a)2 + (y-b)2 = r2 .
However, in this case, a = b = r.
In fact, we can state that the graph of the equation in this form
(x-r)2 + (y-r)2 = r2
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 (x-a)2 + (y-b)2 = r2 :
if a=r, the circle sits on the x axis;
if b=r, the circle sits on the y axis;
|(x-2)2 + (y-4)2 = 42 (x-4)2 + (y-2)2 = 42|