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Math Help - Converting from Parametric to Implicit

  1. #1
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    Converting from Parametric to Implicit

    Hi!

    I was hoping that someone could give me a few guidelines as to how to find the Implicit representation of parametric equations, an example i need to solve has parametric equations,

    x=t^2-t+t and y=t^2+t+1

    I think i should have learnt this last year in my Vector Calculus module but we had problems with a very bad lecturer!

    Thankyou for any replies!
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  2. #2
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    Quote Originally Posted by butterfly View Post
    Hi!

    I was hoping that someone could give me a few guidelines as to how to find the Implicit representation of parametric equations, an example i need to solve has parametric equations,

    x=t^2-t+t and y=t^2+t+1

    I think i should have learnt this last year in my Vector Calculus module but we had problems with a very bad lecturer!

    Thankyou for any replies!
    1. Calculate t wrt x and y:

    \begin{array}{l}x=t^2-t+t  \\ y=t^2+t+1\end{array} Subtract the second equation columnwise from the first on:

    x-y=-2t~\implies~t=-\frac12(x-y)

    2. Plug in this term for t either into the first or the second equation and you'll get:

    \frac14 x^2 - \frac12 xy - \frac12 x + \frac14y^2 - \frac12y +1=0
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  3. #3
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    any chance butterfly is from loughborough? lol
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