Consider the hyperbola x^2/a^2+y^2/b^2 = D (where D is the distance between the foci). Without knowing any specific values of x or y calculate the slope of the asymptote.

Thought: b can solved for and expressed as a complex number. Is its length in the complex plane the same as the desired length in the real plane, that is, is the length of the complex vector b the same as the distance from a focal point on the x axis to the asymptote?