OsculatingEllipse::usage="This simple animation shows how an osculating ellipse acts on a very curious curve.Reference: Personal.";
In[]:=
Manipulated=3;a=d+1d;b=1;​​r[t_]:=(a-b)Cos[t]+bCos
a-b
b
t,(a-b)Sin[t]-bSin
a-b
b
t;δ=ResourceFunction["OsculatingConic"][r[t],{t,θ1},{x,y}];​​p=Grid[{{EQUATION},{Simplify[δ]}},FrameAll,ItemSize->15,ItemStyle->15];​​Show[{ParametricPlot[r[t],{t,0,20π},PlotStyle{Thick,Blue}],ContourPlot[δ,{x,-10,10},{y,-10,10},ContourStyle->{Thick,Red},PerformanceGoal"Quality"],Graphics[{Black,PointSize[0.018],Point[r[θ1]]}]},AxesTrue,AxesOrigin{0,0},BoxRatiosAutomatic,PlotRangeAll,ItemSize900],Style["Osculating ellipse:",Bold,Large],{{θ1,0.01,"Value (θ1)"},0,20π,0.01},Delimiter,p,2,"Equation of the osculating ellipse",ControlPlacementTop
Out[]=
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Osculating ellipse:
Value (θ1)
Equation of the osculating ellipse
EQUATION
7.82863-4.23531x+0.557809
2
x
+5.82936y-0.643319xy+0.766817
2
y
0