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The minor axis of an ellipse can be easily determined , by finding out the smaller axis among the enclosed figure..however the determination of the minor axis of a hyperbola is rather confusing for me.

The both axis of a hyperbola on the transverse axis and the conjugate axis. The 'a' is the point at which the hyperbola intersects the transverse axis. How then will the 'b' be figured when the hyperbola doesn't actually intersect the conjugate axis ?

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Given a hyperbola, one can define its conjugate hyperbola as having the same asymptotes and the same focal distance, but with foci rotated by 90° about the centre. The conjugate axis is then the transverse axis of the conjugate hyperbola.

Intelligenti pauca
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  • If the major and minor axes are inverted for the conjugate hyperbola, why are the terms major and minor used? If the conjugate hyperbola is reference then majaor and minor axes interchange so major is not always larger? – Aurelius Nov 15 '23 at 17:44
  • Terms "major axis" and "minor axis" are indeed meaningless for a hyperbola. It's better to say transverse axis and conjugate axis. – Intelligenti pauca Nov 15 '23 at 18:19