Conic Sections
By Corinne Manogue
Copyright 2009 Corinne Manogue

Initialization

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];

Worksheet

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

Plot the function, 

                                              r(ϕ) = (α/(1+ϵ cos(ϕ+δ)))
  where (r, ϕ) are polar coordinates. First, define the parameters ϵ, α and δ.

ϵ=0.9;
α=3;
δ=0;
PolarPlot[α/(1+ϵ*Cos[ϕ+δ]), {ϕ, 0,2* π}]

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