# 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?

~Kaimbridge~

### Re: Conjugate vs. Transverse Axes/Radii?

The conjugate diameters of ellipse have been defined in
http://planetmath.org/encyclopedia/ConjugateDiametersOfEllipse.html
Similar definitions may be set in hyperbola and parabola.
Jussi

### Incorrect definition

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.