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    Parametric equation help,

    X = t^2 + t

    Y = T^2 - T

    I need to rearrange to get a cartesian equation, but i dont know how to rearrange it when they is a t squred and normal T, I know im being a bit stupid and missing a trick here..
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    (Original post by SunDun111)
    Parametric equation help,

    X = t^2 + t

    Y = T^2 - T

    I need to rearrange to get a cartesian equation, but i dont know how to rearrange it when they is a t squred and normal T, I know im being a bit stupid and missing a trick here..
    Subtract one from the other to get rid of the t^2, then sub back into either.

    OR

    having subtracted one from t'other to get t, add the two to get t^2, and sub the value for t into that.
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    (Original post by SunDun111)
    Parametric equation help,

    X = t^2 + t

    Y = T^2 - T

    I need to rearrange to get a cartesian equation, but i dont know how to rearrange it when they is a t squred and normal T, I know im being a bit stupid and missing a trick here..
    Spoiler:
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    Note that if you add both equations you get:

    x+y = 2t^2 and if you subtract both equations you get x-y = 2t.

    So: y = \frac{x+y}{2} - \frac{x-y}{2}.


    Edit: too slow.
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    I would do it a slightly different way.
     x-y=2t and  x+y=2t^2 so if we divide  (x-y)^2 \text{ by } (x+y)
    you get the cartesian equation to be
     \displaystyle \frac{(x-y)^2}{x+y} = 2
    or
     \displaystyle (x-y)^2=2(x+y) .
 
 
 
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