# How to derive the principal radii of an ellipse

Hi, dear all,

Refer to the attachment, i would like to derive the principal radii of an ellipse, the final equation and figure is provided in Stephen Timoshenko Theory of plates and shells 2nd edition.

consider the ellipse has form b^2*x^2+a^2*y^2=(a^2)*(b^2)
may i know how can i get the correct variable for the red color highlighted length?
because the final equation is so complex, i expect it is not y=2b+unknown.

I use the center as focus origin, the final equation i derive is not correct.as the focus origin move.

In others words , how to get the length for the focus origin as highlighted in red color?

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• derivation of shell in the form an ellipsoid.jpg
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or it is just r1=2b+a?

HallsofIvy
Homework Helper
Your title talks about "principle radii" as if it were a basic property of an ellipse. But the article you show talks about the "principle radii of curvature". That is different at every point and is given by the formula in the article. There is no such thing as a single "principle radius" of an ellipse.

Your title talks about "principle radii" as if it were a basic property of an ellipse. But the article you show talks about the "principle radii of curvature". That is different at every point and is given by the formula in the article. There is no such thing as a single "principle radius" of an ellipse.

Dear HallsofIvy,