(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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).

2. Relevant 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 in to find the parametric equation of the line.

3. 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?

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# Intersection between surfaces

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