Conic sections have a unifying definition: given a point , a line and a real number , the conic having focus , directrix and eccentricity is the locus of all points of the plane such that the ratio between their distance from and their distance from is equal to : .
Change the position of the directrix (by moving points and ), the position of the focus and the eccentricity of the conic to observe what kind of curve you get. Verify that the defining condition on is met for different points . The conic is
- an ellipse when ,
- a parabola when , and
- a hyperbola when .