Question

Suppose you have two hyperbolas that are the same except that the transverse axis and conjugate axis are switched. How does switching the axes affect the equations of the asymptotes for the two hyperbolas? Why?

Answer 1

check the picture below.

assuming both hyperbolas at centered at the origin, the values for the numerator and denominator will switch, so that the slope of one is the reciprocal of the other's slope.