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Thread: x and y

  1. #1
    Member SengNee's Avatar
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    x and y

    $\displaystyle x=t^2+t$
    $\displaystyle y=t^2-t$

    How to find the relation between $\displaystyle x$ and $\displaystyle y$?
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  2. #2
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    Hello, SengNee!

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

    How to find the relation between $\displaystyle x$ and $\displaystyle y$?
    Eliminate the parameter $\displaystyle t.$


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

    Substitute into [1]: .$\displaystyle x \;=\;\left(\frac{x-y}{2}\right)^2 + \frac{x-y}{2}$


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


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