Consider an arbitrary hyperbola without a marked center or foci.
Using only a straightedge and compass construct the transverse and conjugate axes.

(In reply to re(2): Solution by Harry)

So you have to create parallel lines 1 and 2 (with slope m) to create line 3 (with slope m=b²/(a²)) through the center in order to create the hyperbola axes.
Then you create parallel lines 4 and 5 (with slope m=1) to create line 6 (with slope m=b²/a²) through the center in order to help create the asymptotes.

Posted by Bractals on 2014-10-07 22:01:23