1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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


    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


    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


    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


    Staff: Mentor

    Seems like that's an important difference between the graphs of a and c.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Comparing parametric equations
  1. Parametric equations (Replies: 1)

  2. Parametric Equations (Replies: 6)

  3. Parametric Equation (Replies: 3)

  4. Parametric equation (Replies: 10)