Im trying to make an ellipse of a parametric plot in mathematica. This is what I have so far:

x[t_] := 2.5 + 1.5 Cos[π/3 t];
y[t_] := 2.4 + 1.1 Sin[π/3 t];
ParametricPlot[{x[t], y[t]}, {x, 0, 10}, {y, 0, 10}]

My problem is that the range won't change outside of [0,1] for x and y, but the function I have is outside of this; specifically within the region x: [1,4], y: [1,4] which I know because I graphed it on Desmos. I've tried setting the PlotRange option to All, Full, and Automatic, but none of those change anything.

How do I change my range to include the given ellipse?

  • $\begingroup$ You are plotting in a wrong way: see this reference.wolfram.com/language/ref/ParametricPlot.html $\endgroup$ Nov 14, 2019 at 5:39
  • 3
    $\begingroup$ To expand on what @math said, your call to ParametricPlot should specify the range of values for the parameter $t$, not for $x$ and $y$: ParametricPlot[{x[t], y[t]}, {t, 0, 2 Pi}] will plot the ellipse and automatically select an appropriate plot range. $\endgroup$
    – MarcoB
    Nov 14, 2019 at 16:38


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