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Is the distance between lines of latitude the same for an ellipsoid?

I know they are the same for a spheroid and intuitively, I would say it is the same for an ellipsoid but I could not figure out how to calculate this.

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The mathematical solution belongs rather to https://math.stackexchange.com/ but a simple image is challenging your intuition. Look at the ellipsoid and lines at angles of 0, 45, and 90 degrees. What you say would mean that the red segment is as long as the olive green one but obviously it isn't.

enter image description here

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  • Youre using geocentric latitude, whereas (Wikipedia) "latitude" normally means geodetic latitude [en.wikipedia.org/wiki/Latitude] which is the angle of the line normal to the circle.
    – Spacedman
    May 5 '19 at 11:54

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