I discovered the cause of the bug I described in my previous comment. Line 47 of imconicrotation.m does not take into account the sign of 'b' when 'a' == 'c' (i.e. pi/4 or -pi/4). All that has to be done is to change
phi = 0.25*pi;
to be
phi = -0.25*pi*sign(b);
This change solves the problem. I (un)fortunately stumbled upon this due to wanting to rotate an ellipse by -pi/4.
Cheers!

I found that the imconic function incorrectly plots with, at least, the following example:
The following implicit function plots an ellipse with semi-major axis radius or 5 and semi-minor axis radius of 4 and rotated 45 degrees:
20.5*x^2-9.0*x*y+20.5*y^2-400.0
imconic(20.5, -9.0, 20.5, 0, 0, -400.0)
Produces the correct plot.
The following implicit function plots an ellipse with semi-major axis radius or 5 and semi-minor axis radius of 4 and rotated -45 degrees:
20.5*x^2+9.0*x*y+20.5*y^2-400.0
imconic(20.5, 9.0, 20.5, 0, 0, -400.0)
Produces the same plot as the previous implicit function. The plot should appear as shown in this EquationExplorer plot:
http://kevinmehall.net/p/equationexplorer/#20.5*x^2-9.0*x*y+20.5*y^2-400.0|20.5*x^2+9.0*x*y+20.5*y^2-400.0|[-10,10,-10,10]

This is indeed an important package for
computer geometry. A missing link in MATLAB is provided to plot all family members of conic sections in an intuitive manner.
The code is well organized with a handful of examples.

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