My textbook notes that if:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}=1[/tex]

and [tex]a \neq b \neq c[/tex]

Then the ellipsoid is not a surface of revolution. It seems to me though that one can always find a curve in the plane, which when rotated around a line will produce the ellipsoid.

Why is this not true?

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# Ellipsoids and Surfaces of Revolution

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