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)
A more
direct method
After constructing the axesâ€¦
Use points P(2a, 0) on the x axis and Q(2a, sqrt(3)b) on the
curve, to construct a 30^{o}, 60^{o}, 90^{o} triangle
PQR so that
PQ = sqrt(3)b, QR = b, PR = 2b.
Then use the length 2b to construct the point S(2a, 2b) so that
OS is an asymptote.

Posted by Harry
on 20141009 12:08:53 