(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.
The solutions are explained in the attached Word file, in red.
(1) We note that
(a) A line parallel to plane x + y + z = ...
Parametric Equations and the Equation of an Ellipsoid are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.