Geometric Solution of a Quadratic Equation Using Carlyle's Circle

This Demonstration shows the geometric solution of the quadratic equation using Carlyle's circle.

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 .

Drag the black point to change the parameters and .