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Circle alternative parameterization: cannot see whole plot

Posted 10 years ago
parametric plot (r * (1-t^2)/(1+t^2), r * 2×t/(1+t^2)), t=-2..2, r = 10
If one try this query, he'll see incomplete plot. How can I change x and y range of parametric plot?
POSTED BY: Maxim Kamalov
Translating this Maple-like pseudo-code into
(* parametric plot (r*(1-t^2)/(1+t^2),r*2\[Times]t/(1+t^2)),t=-2..2,r=10 *)
With[{r = 10},
ParametricPlot[r/(1 + t^2) {(1 - t^2), 2 t}, {t, -90, 90}, PlotRange -> All]
]
you see it will not really close the circle at {-r,0} because of
In[48]:= r Limit[(1 - t^2)/(1 + t^2), t -> Infinity]
Out[48]= -r

Check your parametrization, you cannot - at least not with Mathematica - do a parametric plot with t reaching from -Infinity to +Infinity.
POSTED BY: Udo Krause
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