How to find formula for rational point ($x$,$y$) on the $y$ = $x^2$ in term of rational parameter $t$. And also how would I write in form of ($x$,$y$) =($f$($t$),$g$($t$))
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1I know that I make $x$ = $t$ and then solve for $y$ – Muneeb Jan 11 '16 at 07:25
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Is there anything else I've to do? – Muneeb Jan 11 '16 at 07:26
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Yes what you are doing seems correct.
Take $x=t$ where $t \in \Bbb Q$. Then $y=x^2=t^2 \Rightarrow y \in \Bbb Q$.
Also it is not true that '$x^2$ is rational $\Rightarrow x$ is rational'.(Take $x^2=2$, then $x=\pm \sqrt 2 \notin \Bbb Q$)
Hence $\{(t,t^2):t \in \Bbb Q\}$ is the set of all rational points on the parabola $y=x^2$.
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