test if a pair of points is conjugate with respect to a sphere
AreConjugate(A, B, s, cond)
Two points A and B are said to be conjugate with respect to the sphere s if the points of intersection P and Q divide A and B harmonically.
The routine returns true if A and B are conjugate with respect to s; false if they are not; and FAIL if it is unable to reach a conclusion.
If FAIL is returned, and the optional argument cond is given, the condition that makes the points conjugate is assigned to this argument.
The command with(geom3d,AreConjugate) allows the use of the abbreviated form of this command.
For what values of ``a'' are the points (-a,2,a), (a,2,3) conjugate with respect to the sphere x2+y2+z2−6⁢x+2⁢y−4⁢z+4=0.
AreConjugate: "unable to determine if -a^2+a is zero"
Hence, the values of ``a'' are
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