Hyperbola (Graph & Equation Anatomy)

Q. Is it possible to tell the location of a hyperbola's center just by looking at its equation? If so, how? Q. How can the length of an hyperbola's transverse axis & conjugate axis be determined just by looking at its equation? Q. What are the key differences in the standard form of the equation of a hyperbola with a horizontal transverse axis vs. a vertical transverse axis?
Questions appear above applet.