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Comparing parametric equations

  1. Nov 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Compare the curves represented by the the parametric equations. How do they differ?
    a.) x =t , y = t^-2
    b.) x = cost , y = (sect)^2
    c.) x = e^t , y = e^(-2t)


    2. Relevant equations
    So I drew them on the calculator they all look like umm... how do I describe this picture the x and y axis ...now picture ...well just picture 1/x^2 that is what they kind look like.


    3. The attempt at a solution

    I'm just having issue coming up with a reasonable explanation. I'm not sure they all pretty much look the same. . Maybe I can say that the rate at which T changes ? So for equation a.) with one change in t you get one change in x and in y you get smaller and smaller changes in it as t increases. Which is slower then say equation b? I don't know
     
  2. jcsd
  3. Nov 6, 2013 #2

    Mark44

    Staff: Mentor

    Think about the point on each graph that corresponds to various values of t, say t = 0. Also think about the orientation. As t increases, which direction does a point move along the curve?
     
  4. Nov 6, 2013 #3

    pasmith

    User Avatar
    Homework Helper

    Note that in (b) you have [itex]-1 \leq x(t) \leq 1[/itex] (and there's a problem with y when [itex]x(t) = 0[/itex]), but in (a) and (c) [itex]x \geq 0[/itex].
     
  5. Nov 6, 2013 #4
    How does a an c differ also? Thanks for response
     
  6. Nov 6, 2013 #5

    Mark44

    Staff: Mentor

    What's the difference in the graphs of x = t vs. x = et, aside from the obvious difference in the shapes?
     
  7. Nov 6, 2013 #6
    Hmm. Well lol one is exponential? I don't know. x = e^t goes faster?
     
  8. Nov 6, 2013 #7

    Mark44

    Staff: Mentor

    Are the domains the same?
     
  9. Nov 6, 2013 #8
    No well x = t is neg to pos inf. and x = e^t is but x will never be 0 here
     
  10. Nov 6, 2013 #9

    Mark44

    Staff: Mentor

    Seems like that's an important difference between the graphs of a and c.
     
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