Find angle of rotation of hyperbola given two asymptotes

Given two asymptotes $$y=m_1x+b_1$$ and $$y=m_2x+b_2$$, and a point on hyperbola $$(p,q)$$ is there a formula for finging an angle of rotation?

I've found a formula (How do I find the slope of an angle bisector, given the equations of the two lines that form the angle?) for finding two possible lines that contain the major axis, but I don't how to use the point to find unique line.

• What angle do you have in mind? Isn't that the slope of the asymptote? Commented Dec 14, 2021 at 14:07
• The axes of the hyperbola are the bisectors of the angles between the asymptotes. Commented Dec 14, 2021 at 14:08
• Thank you. I've found it here: math.stackexchange.com/questions/2084774/… Commented Dec 14, 2021 at 14:15
• Point $(p,q)$ lies in one of the four angles formed by the asymptotes: choose as major axis the bisector lying in the same angle. Commented Dec 14, 2021 at 16:37
• In practice, the sign you must choose in that formula is the same as the sign of $${m_1p-q+b_1\over m_2p-q+b_2}.$$ Commented Dec 14, 2021 at 16:48