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, represent for
alpha > 0 an ellipse.
With the animated variation of lambda (orange line) the yellow radius vector sweeps out the ellipse. This spherical view also shows what happens for large values of lambda.
It may take a some minutes until the graphics appears on your screen!
Compare the Euclidean view.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).