Circles: Equations of a Circle

Graphing Circles on the Coordinate Plane

Now that we know the general equation of a circle, we can begin to graph the equations on the coordinate plane.  When we graph a circle, the center should always be marked and then several points marked which are the appropriate distance away from the center.  It is usually easiest to graph points directly above, below, to the right and to the left of the center.

Example:
Graph the circle (x – 3)2 + (y + 2)2 = 16

Solution:
First, note the center and radius.

C = (3, -2)
r = 4

Now graph the center point and several points that are 4 units away from the center.

Center point 3, negative 2 with points 4 units to the right, to the left, up and down from the center
Center and points 4 units away

The circle will pass through these points.

Circle centered at 3, negative 2 with radius 4
Circle centered at (3, -2) with radius 4