Manipulate[Show[ParametricPlot[
{(Cos[a*t]^n+Sin[b*t]^m+1/c)*Sin[t],
(Cos[a*t]^n+Sin[b*t]^m+1/c)*Cos[t]},{t,0,2\[Pi]}],
Plot[Cos[a*t]^n+Sin[b*t]^m+1/c,{t,0,2\[Pi]},PlotStyle->Dashed],
PlotRange->{{-2.2,2.2},{-2.2,2.2}},ImageSize->Large],
{a,Range[2,4,1]},{b,Range[4,8,1]},{c,Range[4,8,1]},
{n,Range[2,8,1]},{m,Range[2,8,1]}]
(Cos[a*t]^n+Sin[b*t]^m+1/c)*Cos[t]},{t,0,2\[Pi]}],
Plot[Cos[a*t]^n+Sin[b*t]^m+1/c,{t,0,2\[Pi]},PlotStyle->Dashed],
PlotRange->{{-2.2,2.2},{-2.2,2.2}},ImageSize->Large],
{a,Range[2,4,1]},{b,Range[4,8,1]},{c,Range[4,8,1]},
{n,Range[2,8,1]},{m,Range[2,8,1]}]
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