closest point of arbitrary conic to origin in 3D

Robert Lewis lewis at
Wed Sep 11 16:33:25 PDT 2002

     Is anyone aware of symbolic equations to give the point on a conic 
in 3D closest to the origin?  (Assume the conic doesn't touch 0).  The 
conic could have equation

      b1*x^2 + b2*y^2 + b3*z^2 + b4*x*y + b5*x*z + b6*y*z + b7*x + b8*y 
+ b9*z + b10 = 0

    We want a polynomial equation for say, x, that the x coordinate of 
the closest point must satisfy in terms of the symbolic  parameters bi. 
  Similarly for y and z.

Robert H. Lewis
Mathematics Department
Fordham University
New York NY

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