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Math Help - x and y

  1. #1
    Member SengNee's Avatar
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    Pangkor Island, Perak, Malaysia.
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    x and y

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

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

    \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 x and y?
    Eliminate the parameter t.


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

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


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


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