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Math Help - more parametric equations Part 1

  1. #1
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    more parametric equations Part 1

    Eliminate the parameter, t to obtain the cartesian equation in x and y. Sketch the curve, taking note of any restrictions

    a) x = 2at, ~ y = at^2

    b) x = V t \cos a, ~ y = V t \sin a - \frac{g}{2} t^2 where V, g and a are constants

    c) x = t + \frac{1}{t}, ~ y = t^2 + \frac{1}{t^2}


    I know it's a lot and i really dont expect this all to be answered, i just put all the questions which i had serious trouble with and i would be SO grateful to anyone who could give me a few pointers on how to solve these because i just dont know how to get rid of the t OR find the restrictions. again , i know there are alot of questions and im not just expecting answers or a cheap way to get answers for hw, i realli just dont understand it and would seriously appreciate any help .
    thankyou guyz !
    Last edited by mr fantastic; June 7th 2009 at 03:35 AM. Reason: MOved question from original thread, re-formatted equations using latex
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  2. #2
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    Quote Originally Posted by THSKluv View Post
    Eliminate the parameter, t to obtain the cartesian equation in x and y. Sketch the curve, taking note of any restrictions

    a) x = 2at, ~ y = at^2

    b) x = V t \cos a, ~ y = V t \sin a - \frac{g}{2} t^2 where V, g and a are constants

    c) x = t + \frac{1}{t}, ~ y = t^2 + \frac{1}{t^2}


    I know it's a lot and i really dont expect this all to be answered, i just put all the questions which i had serious trouble with and i would be SO grateful to anyone who could give me a few pointers on how to solve these because i just dont know how to get rid of the t OR find the restrictions. again , i know there are alot of questions and im not just expecting answers or a cheap way to get answers for hw, i realli just dont understand it and would seriously appreciate any help .
    thankyou guyz !
    a) x = 2at \Rightarrow t = \frac{x}{2a}. Substitute this into y = at^2.

    b) Similar to a).

    c) x = t + \frac{1}{t} \Rightarrow x^2 = t^2 + 2 + \frac{1}{t^2}. Now substitute y = t^2 + \frac{1}{t^2}.
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