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Parametric equations

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..
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.
(edited 7 years ago)
Reply 2
Avatar for Zacken
Zacken
22
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



Edit: too slow.
Reply 3
Avatar for B_9710
B_9710
18
I would do it a slightly different way.
x−y=2t x-y=2t and x+y=2t2 x+y=2t^2 so if we divide (x−y)2 by (x+y) (x-y)^2 \text{ by } (x+y)
you get the cartesian equation to be
(x−y)2x+y=2 \displaystyle \frac{(x-y)^2}{x+y} = 2
or
(x−y)2=2(x+y) \displaystyle (x-y)^2=2(x+y) .

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