# Carlyle Circle

Carlyle Circle

The Carlyle circle of the quadratic equation -sx+p is the circle with diameter AB, where A = and B = . The points where this circle intersects the axis are the roots of this equation, and the center of the circle is the intersection of the segments AB and CD, where C = and D = .

2

x

(0,1)

(s,p)

x

(s,0)

(0,p+1)