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; |
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| (x-2)2 + (y-4)2 = 42 (x-4)2 + (y-2)2 = 42 |