Question

Find parametric equations for the tangent line to the curve of intersection of the paraboloid
z = x2 + y2
and the ellipsoid
7x2 + 2y2 + 6z2 = 33
at the point
(−1, 1, 2).
(Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Answer 1

(a) study your text, or
(b) google for examples, such as

http://www.math.ucla.edu/~ronmiech/Calculus_Problems/32A/chap12/section6/812d55/812_55.html

and follow the same steps.