Parameterizing xy = 1 for 1 < x < 3

[intenzxboi]

Homework Statement

Give a parameterization for the portion of the graph of xy = 1 for 1 < x < 3

i have no idea what it is asking
x=y

 

[Chaos2009]

A parametric equation is an equation where x and y are expressed in terms of a third variable, usually t. I believe this is what it is asking. Also, xy = 1 does not become x = y.

 

[intenzxboi]

so x+t, 1/y+t?

 

[Chaos2009]

I think you should try looking for something along the lines of:
x = ...
y = ...

 

[intenzxboi]

x=t
y=1/t

so (t, 1/t) 1<t<3

what do i do with this? prof didn't really go over an example like this

 

[sutupidmath]

do you have any info for z?

 

[Dick]

Set x=t, ok? So your first equation is x=t. What's y in terms of t?

 

[sutupidmath]

x=t
y=1/t

so (t, 1/t) 1<t<3

what do i do with this? prof didn't really go over an example like this

this looks good. Is this in R^2 or R^3?

 

[intenzxboi]

i did now what?

 

[Dick]

do you have any info for z?

z? Why z?

 

[intenzxboi]

what do you mean r^2 or r^3?

 

[sutupidmath]

z? Why z?

No particular reason...its just that for some reason i thought we were working in R^3. But, this is not the case since,apparently, we are working in R^2.

 

[sutupidmath]

what do you mean r^2 or r^3?

I didn't write anywhere neither r^2 nor r^3.

 

[Dick]

No particular reason...its just that if we are working in R^3. But, this is not the case since,apparently, we are working in R^2.

Seems so. Carry on.

 

[intenzxboi]

so is that it?
my answer is
x=t
y=1/t

so (t, 1/t) 1<t<3

 

[sutupidmath]

so is that it?
my answer is
x=t
y=1/t

so (t, 1/t) 1<t<3

yep!

 

[intenzxboi]

thanks a lot guys!

 

[Chaos2009]

x = t? Really? You guys are boring.

 

[sutupidmath]

x = t? Really? You guys are boring.

you could have also chosen y=t. or x=u, if you don't like "t's" in particular.

 

[Chaos2009]

I meant you could have made x or y equal to any crazy function in terms of t and it would have still worked, but you guys chose the easiest one. I can't blame you if its for homework, though.

 

[Mark44]

I meant you could have made x or y equal to any crazy function in terms of t and it would have still worked, but you guys chose the easiest one. I can't blame you if its for homework, though.

Sure, you could write it as x = (sin²(t) + cos²(t))t, and y = 1/((sin²(t) + cos²(t))t), but why choose a more complicated parametrization over a simpler one? There is, after all, the principle KISS.

 

[Dick]

Plus picking x=t makes it straightforward to find the t limits corresponding to 1<x<3.