Parameterization of a graph

  • Thread starter intenzxboi
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  • #1
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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
 

Answers and Replies

  • #2
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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.
 
  • #3
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so x+t, 1/y+t?
 
  • #4
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I think you should try looking for something along the lines of:
x = ...
y = ...
 
  • #5
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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
 
  • #6
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do you have any info for z?
 
  • #7
Dick
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Set x=t, ok? So your first equation is x=t. What's y in terms of t?
 
  • #8
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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?
 
  • #9
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i did now what?
 
  • #10
Dick
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  • #11
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what do you mean r^2 or r^3?
 
  • #12
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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.
 
  • #14
Dick
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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.
 
  • #15
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so is that it?
my answer is
x=t
y=1/t

so (t, 1/t) 1<t<3
 
  • #17
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thanks a lot guys!!
 
  • #18
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x = t? Really? You guys are boring. :rofl:
 
  • #19
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x = t? Really? You guys are boring. :rofl:

you could have also chosen y=t. or x=u, if you don't like "t's" in particular.:wink:
 
  • #20
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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.
 
  • #21
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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.
 
  • #22
Dick
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Plus picking x=t makes it straightforward to find the t limits corresponding to 1<x<3.
 

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