Question

The graph of a degenerate circle is a____.

Answer 1

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. .

Answer 2

The graph of a degenerate circle is a point

Which mean :
A point is a degenerate circle (circle equation with zero radius)
for example: ⇒⇒ (x - 2)² + (y - 3)² = 0