In[]:=
Manipulate[Show[{RevolutionPlot3D[{3(1+Sin[t]),4Cos[t](1+Sin[t]),0},{t,0,2π},{θ,0,θ1},RevolutionAxis{1,0,0},PlotStyle->Opacity[0.6],MeshFalse,PerformanceGoal"Quality",ColorFunction"LightTemperatureMap"],ParametricPlot3D[t{1,0,0},{t,-4,9},ColorFunction->"SolarColors"],Graphics3D[{Black,Ball[{5.598076211353316,0,0},0.1]}],Graphics3D[{Black,Ball[{5.598076211353316,3.732050807568878Cos[θ1],3.732050807568878Sin[θ1]},0.1]}],Graphics3D[{Black,Dashed,Thick,Line[{{5.598076211353316,0,0},{5.598076211353316,3.732050807568878Cos[θ1],3.732050807568878Sin[θ1]}}]}]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{1.3,-2.4,2.},ImageSize900],Style["Piriform Surface:",Bold,Large],{{θ1,0.00002,"Value (θ1)"},0.00001,2π,0.00001},ControlPlacementTop]
Out[]=
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Piriform Surface:
Value (θ1)