# Geometric Solution of a Quadratic Equation Using Carlyle's Circle

Geometric Solution of a Quadratic Equation Using Carlyle's Circle

This Demonstration shows the geometric solution of the quadratic equation -ax+b=0 using Carlyle's circle.

2

x

The Carlyle circle of the quadratic equation is the circle with diameter , where and . The points where this circle intersects the axis are the roots of the equation. This follows directly from the trigonometric relations and . You can think of the graphics as the solution of the equation t-atant+b=0.

AB

A=(0,1)

B=(a,b)

x

tan=

θ

1

x

1

tan=

θ

2

x

2

2

tan

Drag the black point to change the parameters and .

B

a

b