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1. The problem statement, all variables and given/known data

Find the shortest distance to the origin given the quadric surface x^2 + y^2 - 2zx = 4

2. Relevant equations

3. The attempt at a solution

F = x^2 + y^2 + z^2

g = x^2 + y^2 - 2zx = 4

Well I initially substituted y^2 = 4 + 2zx - x^2 into F

F = 4 + 2zx + z^2

which leads to z = 0 x = 0 and so y = 2, however this is not the shortest distance. I know this is because of the boundaries of the surface; however I don't know in what way to modify my analysis so that I can take into account the boundaries and get the shortest distance.

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# Homework Help: Shortest distance

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