This is a geometric generation of the conics by the formula |r|=l/(1+epsilon.r1). r1 is the unit vector in the direction of the r. (epsilon.r1) represents the scalar product of the excentricity vector epsilon with r1. l is the semi-latus rectum = |epsilon| |d|.
1/(1+epsilon.r1) is obtained by inversion with a unit circle as mirror. The triangle constructions achieve the necessary division and multiplications.
Change the directrance d (distance focus - directrix) and the green excentricity vector epsilon interactively. This creates the yellow conic (hyperbola, parabola, ellipse, circle) with radius vector r.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).