Is it possible to construct the asymptotes of a hyperbola from the points on the hyperbola by compass and straightedge alone? And if so, how to construct them?
I have no idea how to approach the first question. It seems it should be possible as it is similar to constructing a tangent to an ellipse, but I haven't been able to adjust such a construction to work for the asymptotes of a hyperbola. An illustration or a reference would be welcome.