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What is the sum of focal radii of a vertical ellipse? In my textbook it says 2a but online it says it's 2b. I think it's 2b but I don't get why it's different in my textbook. Also, what is the equation of a vertical hyperbola? It's different from in my textbook and in the UCLA textbook for conic sections; in UCLA it says y^2/b^2 - x^2/a^2, but in my textbook it says y^2/a^2 - x^2/b^2. I asked someone and they said there's no difference but I'm pretty sure they're wrong because I tested it out in desmos and they were completely different. And, what is the difference of focal radii of a vertical hyperbola? Is it 2a or 2b? It says 2b online. Please help!!

Noura
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    It depends upon whether you use "$a$" and "$b$" to mean "semi-major axis" (aks, "major radius") and "semi-minor axis" ("minor radius"), respectively, or "horizontal semi-axis" and "vertical semi-axis". (Both are valid.) ... There was a question about this kind of thing not too long ago. I'll see if I can find it instead of re-hashing the discussion here. – Blue Jan 30 '20 at 16:57
  • I found the question: "Confusion regarding usage of 'a and b' in an ellipse", There are no answers, per se, just comments (including my own). Perhaps they'll help a bit. Of course, you are free to ask for further/better clarification. – Blue Jan 30 '20 at 17:05
  • Well, I say that the equation of a vertical hyperbola is $(mx+y)(mx-y)=k$, with $k\lt0$, so there’s no $a$ and $b$ to worry about. As Blue says, it all depends on what the parameters mean, and different authors will use different conventions. – amd Jan 30 '20 at 17:08

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