r[θ_,ekscentricitet_]:=(1/(1+ekscentricitet Cos[θ]))

Mathematica 5

<<Graphics`Graphics`

PolarPlot[r[θ,0.8],{θ,0,2π}]

PolarPlot[r[θ,1.0],{θ,-0.9π,0.9π}]

Mathematica 6

Manipulate[PolarPlot[r[θ,e],{θ,0,2π}],{e,0,1.5}]