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

I am asked to find the curve of intersection between x^2 + y^2 + z^2 = 36 and 2x + y -z = 2.

2. Relevant equations

3. The attempt at a solution

I know the first equation is a sphere of radius 6, and the second equation will pass through it, so when projected on the xy plane it will also be an ellipse. I'm just not sure how to go about solving for the (x,y) coordinates, so that I know the curve of the line. My guess would be to solve for z in both equations and set them equal to each other. However, when I do that I end up with something ugly...

36 = 5x^2 + 2y^2 + 4xy -8x -4y + 4

Then I'm stuck...

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# Homework Help: Curve of Intersection

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