Conic sections defined by excentricity
- Przemysław Kajetanowicz
Consider a straight line in the plane and a point such that . Consider the set of all points in the plane such that the ratio is constant, where stands for the distance of the point from the line . The following then holds. If then is an ellipse. If then is a parabola. If then is a hyperbola. The line is called the directrix of the curve. The point is called the focus and is called the excentricity of the curve. Use the mouse to move the point in the illustration. Study the picture to observe that the excentricity actually remains constant. Its value is equal to the tangent of the angle (the circular arc has been added to highlight the latter fact). It is easy to visually inspect the invariability of , and so also the invariability of ). Note: to precisely control the value of by the appropriate slider, you may need to use arrow keys rather then the mouse.