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How much hyperbola should one study in order to be prepared for the final exam?

{For instance, is it necessary to know how to intersect hyperbolic lines at certain angles?}

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I am assuming by "hyperbola" you mean "hyperbolic geometry". The first question: you should know and understand the topics we have covered. The questions in the final will be based on that material. Second question: You should know how to construct a hyperbolic line intersecting another at a right angle; we will not go beyond that.