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$(x/3)^2+(y/5)^2=1$, $x=3\sin[t]$, $y=5 \cos[t]$

I want to draw a phase trajectory with time-lapse using manipulate or animate.

Manipulate[ParametricPlot[(x/3)^2 + (p/5)^2 == 1, {x, -3, 3}, {p, -5, 5}], {t, 0, 10}] I tried this code. It is not working. What is the proper version?

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  • $\begingroup$ Try ContourPlot but parametric version of the equation + ParametricPlot will be more efficient. $\endgroup$
    – Kuba
    Oct 22 '20 at 6:27
  • $\begingroup$ I mean manipulating the time ellipse needs to be drawn. Not asking how to draw an ellipse. $\endgroup$
    – Tursinbay
    Oct 22 '20 at 6:33
  • $\begingroup$ Sorry, I am confused as to what do you want to plot. For given t the equation does not represent the ellipse, it is just True/False. $\endgroup$
    – Kuba
    Oct 22 '20 at 6:43
  • $\begingroup$ ParametricPlot[{3 Sin[t],5 Cos[t]} ,{t,0,10}] $\endgroup$ Oct 22 '20 at 7:00
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    $\begingroup$ Something like this? Manipulate[ParametricPlot[{3 Sin[t], 5 Cos[t]}, {t, 0, tMax}, PlotRange -> {{-3, 3}, {-5, 5}} ], {tMax, .01, 2 \[Pi]}] $\endgroup$
    – Natas
    Oct 22 '20 at 7:04

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