flyingpig
- 2,574
- 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
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
\frac{y^2}{b^2}- \frac{x^2}{a^2}= 1
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 xy = 1 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 \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
Now I am going to rewrite it as y = \pm \frac{b}{a}\sqrt{x^2 - a^2}
Now I just want to look at \sqrt{x^2 - a^2}
How do I recognize that \sqrt{x^2 - a^2} 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.