Question

Given any arbitrary hyper-ellipsoid defined by an orthonormal basis, center and extents along each axis, calculate the global maximum of the curve bounded by any arbitrary vector V, and the perpendicular plane P to V, where both V and P intersect the each other and the hyper-ellipsoid.

Answer 1

Do you know the standard equation of the ellipsoid? .. that will help.

Answer 2

So I should implicitly differentiate the bounded curve of the equation of an ellipsoid to find the maximum? What about its arbitrary orientation?

Answer 3

First you setup the ellipsoid from the conditions, then find critical points based on D=f_xx*f_yy-f_xy*f_yx, D>0 where f_xx>0. Then put each critical point, plus the end points into the original ellipsoid to the greatest value, which is the global maximum.