- #1

flyingpig

- 2,579

- 1

## Homework Statement

I`ll try to make this as orderly as possible, but I've got so many questions about it

1. The most "general" form of a hyperbola are

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

[tex] \frac{y^2}{b^2}- \frac{x^2}{a^2}= 1[/tex]

Now my question is, the first one opens with the x-axis, the second one opens with the y-axis. My question is, I am never going to be able to rememeber them, even if i draw out my asympotetes I am not going ot be able to deduct with which axis does the hyperbola open.

Also just another side question, the asympotetes are negatives of each other, but when I graphed it, they are also perpendicular to each other. Now here is the thing, how come they aren't negative reciprocal of each other?

2. Sometimes we call [tex]xy = 1[/tex] as a hyperbola how do I convert those from (1) to this form?

3. How do the hyperbolic functions apply to (2)?

4. I never understood this, that's say [tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Now I am going to rewrite it as [tex]y = \pm \frac{b}{a}\sqrt{x^2 - a^2}[/tex]

Now I just want to look at [tex]\sqrt{x^2 - a^2}[/tex]

How do I recognize that [tex]\sqrt{x^2 - a^2}[/tex] will give me a curve and not a straight line? I used to think that the square and the square root "cancels" and the a doesnt' matter. I was wrong.