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.
Compare the Euclidean view.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).