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Graphics << Implicit vs ContourPlot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122738] Graphics << Implicit vs ContourPlot
  • From: John Accardi <johnaccardi at comcast.net>
  • Date: Wed, 9 Nov 2011 06:24:00 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Goal: Show students a plot of both an ellipse with x axis as ellipse's 
transverse axis
and the same ellipse in an x'y' coordinate plane that is rotated some angle
with respect the the original xy coordinate plane.  (All in one plot)

I used:

<< Graphics`ImplicitPlot`; ImplicitPlot[{7 x^2 - 6 Sqrt[3] x y +
     13 y^2 - 16 == 0, ((x^2)/2^2) + ((y^2)/2^2) == 1, y == x,
   y == -x}, {x, -3, 3}, AspectRatio -> 1.25]

which works well but I had to hard fix the axis of rotation at 45 degrees
and plot it (y == x and y == -x).  I also get an obsolete warning and
the suggestion to use the new ContourPlot for this in the future:

General::obspkg: "\!\(\"Graphics`ImplicitPlot`\"\) is now obsolete.
The legacy version being loaded may conflict with current Mathematica
functionality. See the Compatibility Guide for updating information."

So I try to accomplish the same graph with ContourPlot:

ContourPlot[{7 x^2 - 6 Sqrt[3] x y + 13 y^2 - 16 ==
    0, ((x^2)/2^2) + ((y^2)/2^2) == 1, y == x, y == -x, y == 0,
   x == 0}, {x, -3, 3}, {y, -3, 3}, AspectRatio -> 1.25]

which gets me close but I have lost traditional plotting of the xy axes
(no tick marks).  Instead I get ContourPlots boxed style coordinate system.

Question: How can I get my old style axes back in the context of 
ContourPlot?

Thank you for any insights.
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