What is the Hyperbola of Apollonius?

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The discussion clarifies that Apollonius named the conic sections, including hyperbolas, which relate to slicing an oblique cone. The term "hyperbola of Apollonius" specifically refers to a rectangular hyperbola associated with a particular point and conic. While all hyperbolas of Apollonius are rectangular, the phrase alone lacks a definitive meaning without context. The conversation emphasizes the connection between Apollonius's work and the classification of hyperbolas. Understanding this terminology is crucial for studying conic sections in mathematics.
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Simple question. Is what we now call a 'rectangular hyperbola' what was once called the hyperbola of Apollonius? Thanks
 
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Hi ralphiep. :smile:

As far as I know Apollonius was the one who named the conics, i.e parabola, ellipse, and hyperbola. He related them to the well known analogy of slicing an oblique cone. That obviously includes the regular(non rectangular) hyperbolas.
 

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