For the hyperbola, they can switch, but it has nothing to do with if b>a. You switch a and b around when you're working with the inverse function, that is, when y<SUP>2</SUP>/b<SUP>2</SUP> - x<SUP>2</SUP>/a<SUP>2</SUP> = 1 . That hyperbola goes up and down, rather than left and right.