Bitangent

Author

Eric W. Weisstein
April 22, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/Bitangent.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Bitangent.html.

©2013 Wolfram Research, Inc. except for portions noted otherwise

Examples

Plücker

Gray’s modification

ContourPlot[(x+y)(y-x)(x-1)(x-1.85)-5(y^2+x(x-2))^2==0,{x,-.5,2.5},{y,-1.5,1.5},AspectRatio->Automatic,MaxRecursion->5]

Plücker’s original = Ampersand curve

Factor[{(x+y)(y-x)(x-1)(x-(3/2)),2(y^2+x(x-2))^2}]

ContourPlot[(x+y)(y-x)(x-1)(x-(3/2))-2(y^2+x(x-2))^2==0,{x,-.5,2.5},{y,-1.5,1.5},AspectRatio->Automatic,MaxRecursion->5]

Trott Curve

g1=ContourPlot[12^2(x^4+y^4)-15^2(x^2+y^2)+350x^2y^2+81==0,{x,-1,1},{y,-1,1},ContourStyle->Red,Frame->False,Axes->True]

g2=;

GraphicsRow[{g1,g2/.l_Line:>{Thickness[.003],l}}]