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conjugate points

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Is the poles being "conjugate points" from which the y-axis of an ellipse/spheroid is considered the conjugate axis/diameter?:

If so, then how can "ConjugateDiametersOfEllipse" be?:

Aren't they actually "oblique diameters"?
In "A treatise on analytical geometry", on pg.199, conjugate and transverse axes are noted, regarding oblate and prolate spheroids:

But, back on pg.107, the above concept of "ConjugateDiametersOfEllipse" appears to being discussed

How can that be? Are these two different meanings of "conjugate diameter?


The conjugate diameters of ellipse have been defined in
Similar definitions may be set in hyperbola and parabola.

Conjugate points need not have more than one geodesic connecting them.

The correct definition is the existence of a non-trivial Jacobi fields along a geodesic between the two points and vanishes at both points.

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