Compute the minimum distance between the centre to the curve $xy=4$. I wish to solve the following problem: 

Compute the minimum distance between the center to the curve $xy=4$.

But I don't know where to start from?

You need to minimize the function
$$d= \sqrt{x^2 +y^2} = \sqrt{x^2+ 16/x^2}.$$
Which we got by considering the distance from a point on the curve to the origin. Now, use the derivative test. See related problem.
