Manipulate[PolarPlot[Sin[t]^2/(1-b*Cos[t])^5,{t,0,2Pi},PlotRange->All],{b,0,1}]

Manipulate[PolarPlot[((1-b*Cos[t])^2-(1-b^2)Sin[t]^2*Cos[phi]^2)/(1-b*Cos[t])^5,{t,0,2Pi},PlotRange->All],{b,0,1},{phi,0,2Pi}]

b=1-e
Series[((1-b*Cos[t])^2-(1-b^2)Sin[t]^2)/(1-b*Cos[t])^5,{t,0,2}]