When the coordinates of a point are on the quadric
(7)
and expressed in terms of the parameters and of the confocal quadrics passing through that point (in other
words, having ,
,
,
and ,
,
for the squares of their semimajor axes), then the equation of a geodesic
can be expressed in the form
(8)
with
an arbitrary constant, and the arc length element is given by
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