My question is somewhat dumb but for some reason I haven't been able to come up with an answer. Why is the hyperbola round at the bottom? Namely, I'm thinking of any of these two equations x^2-y^2=1 or y^2-x^2=1 These two behave like a line as you approach infinity but then becomes round at the bottom. Why do they behave roundy at the bottom? edit: I completely understand why this must be the case if I consider the hyperbola as a conic section. But I'm specifically talking about the equation for a hyperbola.