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I have already looked at this answer but couldn't figure out how to use it in my case, particularly due to needing to include the orientation. I currently have a value for my axial ratio and a value for my orientation, and that is all. The size is irrelevant due to prior normalization. I feel like I am just missing something in the other question, but don't know what it is, this kind of math isn't my forte. Thanks in advance.

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    $\begingroup$ "a value for my orientation" - by this, you mean the angle of the major axis from the horizontal? $\endgroup$ – J. M. will be back soon Mar 31 '16 at 6:24
  • $\begingroup$ Yes, that is what I have. $\endgroup$ – Adrian Smith Mar 31 '16 at 20:13
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a = 5; b = 3;
ϕ = π/6;
ParametricPlot[{a Cos[t] Cos[ϕ] - b Sin[t] Sin[ϕ], 
a Cos[t] Sin[ϕ] + b Sin[t] Cos[ϕ]}, {t, 0, 2 π}, 
PlotRange -> All, PlotStyle -> Directive[Thick, Red]]

enter image description here

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