- #1
bodensee9
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Homework Statement
Hi, I need help with the following. I'm asked to find the parametric equation of the tangent line to the curve of the interrsection of the paraboloid z = x^2 + y^2 and the ellipsoid 4x^2+y^2+z^2 = 9 at the point (-1,1,2).
Homework Equations
I think I'm asked to find the gradient of the curves of the intersection, and then I know the vector with the direction of the line eof intersection, and then I can plug it back into find the parametric equation of the line.
The Attempt at a Solution
I guess I am trying to find the equation of the curve of intersection first? So, would I set the two equations equal so that I would get 4x^2+y^2+(x^2+y^2)^2 = 9? But then z has gone away? I guess I'm pretty clueless as to how to attempt to solve this problem?
Or if I'm right that the intersection is an ellipse, but how am I supposed to find the equation of the ellipse? Can anyone give me any pointers or hints?