Finding Asymptotes for a Hyperbola in Standard Form

[nameVoid]

Sketching the graph of xz=4
Z=4/x
Now this is not in the form of a hyperbola however it is indeed a hyperbola
I get this by taking x to 0 and infinity
My question is how to put it in the standard form of a hyperbola to find the equations of the aysmptope

 

[micromass]

What is your standard form of a hyperbola?

Did you study a lot of linear algebra? Do you know how to change the basis?

 

[Matterwave]

You should make a 45 degree rotation of your x and y axes. In other words, define:

$$u=\frac{x+z}{\sqrt{2}}$$
$$v=\frac{x-z}{\sqrt{2}}$$

And see where that takes you.

 

[micromass]

You should make a 45 degree rotation of your x and y axes. In other words, define:

$$u=\frac{x+z}{\sqrt{2}}$$
$$v=\frac{x-z}{\sqrt{2}}$$

And see where that takes you.

I would have preferred the OP to have found this on his own. Now he has no idea where those formulas came from.

 

[Matterwave]

Ah, that's my bad...I will be more discreet in the future.

 

[nameVoid]

I'm still waiting for the explanation

 

[micromass]

I'm still waiting for the explanation

Well, I've asked you questions which you seemed to ignore.

Second, Matterwave has given you a very large hint. Try to use the hint to work it out for yourself. We're certainly not going to spoonfeed you the answer.

 

[LCKurtz]

@namevoid: It would be good to give a complete and exact statement of the problem. Your use of $x$ and $z$ suggests perhaps this is a surface in 3D. Or not?? Also is part of the problem to put it in standard form or do you want to do that just to find the equations of the asymptotes?