In the book COORDINATE GEOMETRY of THREE DIMENSIONS' (1937) of
Robert J.T. Bell there is a statement (EX.1. p. 178) that
the primary semi-axes a[1], a[2] and a[3] of the confocals of
x^2/a^2 + y^2/b^2 + z*2/z^2 = 1through a point (alpha, beta, gamma) satisfy
the equations
alpha^2 = (a[1]*a[2]*a[3])^2/(b^2-a^2)/(c^2-a^2)
beta^2 = - (b^2-a^2+a[1]^2)*(b^2-a^2+a[2]^2)*(b^2-a^2+a[3]^2)//(a^2-b^2)/(c^2-b^2)
gamma^2 = (c^2-a^2+a[1]^2)*(c^2-a^2+a[2]^2)*(c^2-a^2+a[3]^2)//(b^2-c^2)/(a^2-c^2)
I'm trying to solve these equations for a[1], a[2] , a[3] and check the result by substituting it in the above equations by computer. The first and second equations give fine results. However, the third does not. Perhaps an error? Of course, probably I made an error
Perhaps there is a fool like me wasting his time the way I do.
Nevertheless, your comment will be appreciated.
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