Find Closest Point on Hyperbola: xy=8 to (3,0)

[karisrou]

1) Find the point on the hyperbola xy=8 closest to (3,0).

I honestly, have no idea what to do. I seriously do not remember discussing anything like this in class, nor having any previous problems in homework. If anyone can give me a start or walkthrough, that would be fantastic!

 

[Wretchosoft]

Well, y = 8/x gives you a relation between the two variables that allows you to write the distance from (x,y) to (3,0) in terms of one variable, which can then be easily minimized.

 

[karisrou]

I've got D = 2rtx^2 - 6x + 9 + 64/x^2

I'm not sure as to how this minimizes?

 

[HallsofIvy]

HOW did you get that? What are r and t? What is D? There were not "r", "t", or "D" in your orginal statement of the problem.