Hyperbola as parametric second order curve (Euclidean view)

The parametric second order curve
r = (a0 + a1 lambda + a2 lambda lambda)/(alpha + lambda lambda),
with a0, a1 and a2 three arbitrary vectors and alpha, lambda scalars, represents for
alpha < 0 a hyperbola.

With the animated variation of lambda (orange line) the yellow radius vector sweeps out the hyperbola.

It may take some minutes until the graph below appears!

Please enable Java for an interactive construction (with Cinderella).

Compare the sperical view.

[ conics | GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).