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geom3d[AreConjugate] - test if a pair of points is conjugate with respect to a sphere
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Calling Sequence
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AreConjugate(A, B, s, cond)
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Parameters
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s
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a sphere
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A, B
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two points
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cond
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(optional) name
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Description
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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.
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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.
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If FAIL is returned, and the optional argument cond is given, the condition that makes the points conjugate is assigned to this argument.
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The command with(geom3d,AreConjugate) allows the use of the abbreviated form of this command.
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Examples
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For what values of ``a'' are the points (-a,2,a), (a,2,3) conjugate with respect to the sphere x^2+y^2+z^2-6*x+2*y-4*z+4=0.
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![sphere(s, x^2+y^2+z^2-6*x+2*y-4*z+4 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5435/file03967/math113.png)
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AreConjugate: "unable to determine if -a^2+a is zero"
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Hence, the values of ``a'' are
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check:
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