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Let $x(t) = \frac{1-t^2}{1 + t^2}$ and $y(t) = \frac{2t}{1+t^2}$

What curve does this represent as $t$ varies over $[−1, 1]$?

My attempt: I suspect it represent parabola. I know that by trigonometry formula $\sin2A = \frac{2\tan A}{1+\tan^2 A} =\frac{2t}{1+t^2}$. But here I used the graph of $\sin2A$, it look parabola, and $\cos2A = \frac{1-\tan^2A}{1+\tan^2A} =\frac{1-t^2}{1+t^2}$, similarly it also look like parabola.

If anybody help me ,,i would be very thankful,,

Kenny Lau
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    $x^2 + y^2 = 1$ – Kenny Lau Sep 01 '17 at 06:55
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    $\sin^2 2A + \cos^2 2A = 1$ – Kenny Lau Sep 01 '17 at 06:55
  • Parabolas are quadratic. – Kenny Lau Sep 01 '17 at 06:55
  • Thanks keny Lau@ ok,,but i don"t know,, –  Sep 01 '17 at 06:57
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    You may be drawing the y parabola on paper with one hand, but with the other hand you are pulling the paper at a non-constant speed. – Pieter21 Sep 01 '17 at 07:16
  • Other lego legoh's have been placed in question-ban. Are they your siblings or are you trying to work around the rules by creating more accounts to be able to ask more bad questions? – Jyrki Lahtonen Sep 01 '17 at 07:16
  • @JyrkiLahtonen But this question seems to be OK according to rules of this website. Do we have any problem if this user has created another account to ask a not-bad question? – Jaideep Khare Sep 01 '17 at 07:19
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    @JaideepKhare That is an interesting question. An attempt to circumvent a ban is obviously against the rules. On the other hand it might be ok to allow a fresh start, for the official way of getting out of a question ban is a bit taxing (for a good reason). A problem is that in the present case this may be "a fresh start number three". You see the problem :-) – Jyrki Lahtonen Sep 01 '17 at 07:23
  • @James lego legoh ; see each of the followings: https://math.stackexchange.com/questions/1958573/is-it-possible-to-elementarily-parametrize-a-circle-without-using-trigonometric/1958581#1958581 https://math.stackexchange.com/questions/255615/parametric-equation-of-a-circle-using-a-line/255626#255626 https://math.stackexchange.com/questions/509028/equation-of-a-circle-from-parametric-functions-of-sin-and-cos/509030#509030 – Davood Sep 01 '17 at 07:28
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    Thanks a lots @Famke ,,god bless u –  Sep 01 '17 at 07:29

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