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My maths teacher is teaching hyperbola these days, and when he drew the hyperbola, I was not able to see $b$ (in $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$) in the graph. When I asked about it, all he did was just marked the points $(0,b)$ and $(0,-b)$. I expected a lot more, but sir just said $b$ according to him has an indirect significance ($a^2+b^2=(ae)^2$). I'm still not satisfied. Is $b$ just a number?

Blue
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Rohinb97
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  • Right, $b$ is just a number. Also, the "hyperbolic geometry" tag doesn't apply here. – tylerc0816 Nov 23 '13 at 11:23
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    The asymptotes of the hyperbola are $\frac{x}{a} \pm \frac{y}{b} = 0$, aka $y = \pm\frac{b}{a} x$. That is, the asymptotes are the extended diagonals of the origin-centered rectangle with "semi-width" $a$ and "semi-height" $b$. – Blue Nov 23 '13 at 11:42
  • BTW: Here's a bit more on the geometry of the hyperbola and the relation $a^2+b^2=c^2$ from the conic section interpretation of the hyperbola: http://math.stackexchange.com/a/409149/409 – Blue Nov 24 '13 at 14:56

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