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# Parametric Equations and Equation of an Ellipsoid

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(1) Find parametric equations for the line through the point (0, 1,2) that is parallele to the plane x+y+z = 2 and perpendicular to the line x = 1 +t, y = 1 ?t,z = 2t.
(2) An ellipsoid is created by rotating the ellipse 4x2 + y2 = 16 about the x-axis. Find an equation of the ellipsoid.

See the attached file.

##### Solution Summary

Parametric equations and the equation of an ellipsoid are investigated. The solution is detailed and well presented.

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The solutions are explained in the attached Word file, in red.
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Solutions:

(1) We note that
(a) A line parallel to plane x + y + z = ...

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