There are two kinds of degeneracy that occur in circles.
1. Consider the equation of circle
x² + y² - 2 x - 2 y +2=0
(x-1)² + (y-1)²=0
The circle having Zero radius is case of degeneracy. The graph of the circle having Zero radius is a point.
2. Consider another circle
x² + y² - 2 x + 2 y +8 =0
(x-1)² + (y +1)²-1-1+ 8=0
(x -1)² + (y +1)²= -6= [i√6]²
This is a circle having negative radius.As we can't predict the radius of circle , so Circle having infinite radius will have the graph of straight line. .
