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