# What does “$b$ - length of semi-conjugate axis” represent in the graph of hyperbola?

In the standard equation of hyperbola, $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ where $$b^2=a^2(e^2-1)$$

If I were to draw the graph of hyperbola what would it represent in the graph? As $$a$$ represents the distance of vertex from the origin.

• $\pm b/a$ are the slopes of the hyperbola's asymptotes. (Note: Whereas $a$ is called the "transverse" (semi)axis of the hyperbola, $b$ is the "conjugate" (semi)axis, which is the transverse (semi)axis of the conjugate hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$$ which has the same center and asymptotes but opens "up and down".) – Blue Apr 1 '16 at 6:15
• @Blue I don't think that really answered the question . I don't see how does it represent anything on the graph :/ Well, maybe it did as amd explained. It's just that I think there should be something more then that – brainst Apr 1 '16 at 6:19
• Why not trying it ? geogebra Basically it's not a cycle, and looks like an hourglass – Aseed Apr 1 '16 at 6:25

## 1 Answer

This is the length of the segment perpendicular to the major axis from vertex to either asymptote. Thus, as Blue notes, the asymptotes have slope $\pm\frac b a$.

• that's it? that property doesn't look like fun :( – brainst Apr 1 '16 at 6:22
• @brainst Well, it’s also the length of the semimajor axis of the conjugate hyperbola, but, yeah, that’s about it. – amd Apr 1 '16 at 6:40