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Math Help - Parametric to rectangular equations

  1. #1
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    Parametric to rectangular equations

    Is this the correct strategy to convert this parametric to rectangular? Do I need to further simplify the answer or is this good enough?

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  2. #2
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    A correct strategy has two important features:

    1) You understand it and can communicate it.
    2) It works and doesn't mess up the Domain.

    I think you have it.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by CrazyLond View Post
    Is this the correct strategy to convert this parametric to rectangular? Do I need to further simplify the answer or is this good enough?

    Probably a better way would be this

    x=t^2+t=\left(t+\frac{1}{2}\right)^2-\frac{1}{4}

    So solving for t we get

    t=\pm\sqrt{x+\frac{1}{4}}+\frac{1}{2}

    Now imput that into your y
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  4. #4
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    Hello, CrazyLond!

    Yet another approach . . .


    \begin{array}{cccc}x &=&t^2+t & [1] \\ y &=&t^2-t & [2] \end{array}

    Subtract [1] - [2]: . x-y \:=\:2t\quad\Rightarrow\quad y \:=\:\frac{x-y}{2}

    Substitute into [2]: . y \:=\:\left(\frac{x-y}{2}\right)^2 - \left(\frac{x-y}{2}\right)


    This simplifies to: . x^2 - 2xy + y^2 - 2x - 2y \:=\:0


    I believe this is the parabola: y^2 = \sqrt{2}\,x rotated 45 CCW.
    . . (But don't quote me!)

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