A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of the sphere OABC is (ax)23 + (by)2/3 + (cz)2/3 = (x² + y² + z?)2/3. %3D

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 7E: Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a...
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A tangent plane to the ellipsoid
x² y? z2
a?
meets the axes in A, B, C. Show that the envelope of the sphere OABC is
(ax)2/3 + (by)2/3 + (cz)2/3 = (x² + y² + z?)2/3.
62
%3D
Transcribed Image Text:A tangent plane to the ellipsoid x² y? z2 a? meets the axes in A, B, C. Show that the envelope of the sphere OABC is (ax)2/3 + (by)2/3 + (cz)2/3 = (x² + y² + z?)2/3. 62 %3D
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