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Geometric Solution of a Quadratic Equation Using Carlyle's Circle

​
This Demonstration shows the geometric solution of the quadratic equation
2
x
-ax+b=0
using Carlyle's circle.
The Carlyle circle of the quadratic equation is the circle with diameter
AB
, where
A=(0,1)
and
B=(a,b)
. The points where this circle intersects the
x
axis are the roots of the equation. This follows directly from the trigonometric relations
tan
θ
1
=
x
1
and
tan
θ
2
=
x
2
. You can think of the graphics as the solution of the equation
2
tan
t-atant+b=0
.
Drag the black point
B
to change the parameters
a
and
b
.
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