Conic Sections

SetOptions[PolarPlot,BaseStyle->{FontFamily->"Arial",FontSize->16},PlotStyle->{{Black,AbsoluteThickness[1.5]}},AxesLabel->{"x","y"},AxesStyle->Directive[FontFamily->"Arial",FontSize->16,Black,AbsoluteThickness[0.5],Arrowheads[0.04]],TicksStyle->{{Black,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[0.5]}},ImageSize->500];

In this worksheet you will look at the graphs of a family of curves written in polar coordinates r, ϕ.  

Below, we plot the function, 
                                              r(ϕ) = (α/(1+ϵ cos(ϕ+δ)))
where (r, ϕ) are polar coordinates.

By pressing the small [+] next to each slider, you can view the values of ϵ, α, and δ.

Manipulate[PolarPlot[α/(1+ϵ*Cos[ϕ+δ]), {ϕ, 0,2* π},PlotRange->{{-5,5},{-5,5}}],{{ϵ,.5},-2,2,0.01},{{α,1},0.5,2,0.01},{δ,0,2*Pi}]

Try different values for ϵ, α, and δ.    What shapes do you get?

By Corinne Manogue