Carlyle Circle

s parameter

p parameter

The Carlyle circle of the quadratic equation

2

x

-sx+p

is the circle with diameter AB, where A =

(0,1)

and B =

(s,p)

. The points where this circle intersects the

x

axis are the roots of this equation, and the center of the circle is the intersection of the segments AB and CD, where C =

(s,0)

and D =

(0,p+1)

.