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