Shortest Distance from Curve to Origin: How to Minimize x^2+y^2?

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Homework Statement

Find the shortest distance from [tex]x^{2}-y^{2}=1[/tex] and the origin.

I was gone when my professor taught on this. I just want some hints to get started...

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The Attempt at a Solution

I graphed it and it's pretty easy to see that the answer is one. I just don't know how to prove it...
 
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The square of distance is x^2+y^2, so you have to minimize that. Can you express x^2+y^2 in terms of only one variable?