What is a quick way to determine whether a shape is a parabola or a hyperbola. I realize that hyperbolas consist of two arcs. I guess my question is this: Is a hyperbola two parabolas back to back? Also 1/x is an arc, so is it a parabola or hyperbola. I thought of this question after playing Robot Unicorn Attack which involves what I think is a parabola, but it may very well be one arc of a hyperbola. I am aware of the equations relating to these conic sections, but 1/x does not fit into any of these formulas, plus it is rotated. For reference: a parabola uses this equation: y-k=a(x-h)^2. Hyperbolas use this equation (x-h)^2/a^2 - (y-k)^2/b^2 = 1. If you can help me out please do. Any help is appreciated. Cheers.