( 786, #91) The ellipsoid intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point ( 1, 2, 2).

Solution:

When y = 2, the equation of the ellipsoid formed in the plane y = 2 is:

Parameters for the ellipse are:

and for its tangent line are:

Thus at the point ( 1, 2, 2 ) , and the parametric equations for the tangent line are:

There are equivalent parametric equations for the tangent line, e.g. x = 1 + t, y = 2, z = 2 - 2t obtained by replacing t in our representation by -t.

No Maple Code for this problem.

by: nl