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

  • Thread starter Thread starter karisrou
  • Start date Start date
  • Tags Tags
    Hyperbola Point
Click For Summary

Homework Help Overview

The problem involves finding the point on the hyperbola defined by the equation xy=8 that is closest to the point (3,0). Participants express uncertainty about the approach to take, indicating a lack of familiarity with similar problems.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant suggests using the relation y = 8/x to express the distance in terms of a single variable for minimization. Another participant questions the variables and terms introduced in a distance formula, indicating confusion about the notation used.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the validity of the expressions presented. There is no clear consensus yet, but some guidance has been offered regarding the relationship between the variables.

Contextual Notes

Participants note a lack of prior exposure to similar problems in class or homework, which may affect their confidence in approaching the task.

karisrou
Messages
15
Reaction score
0
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!
 
Physics news on Phys.org
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.
 
I've got D = 2rtx^2 - 6x + 9 + 64/x^2

I'm not sure as to how this minimizes?
 
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.
 

Similar threads

What is the interval for a so that the given line is normal to the hyperbola?
  • · Replies 4 ·
Replies
4
Views
2K
Finding Polar Equation for hyperbola with Graph xy=16
  • · Replies 3 ·
Replies
3
Views
2K
Find the point on the curve y=√(4x) that is closest the the point (3,0)
  • · Replies 3 ·
Replies
3
Views
6K
Finding a point on a surface which is closest to given point
  • · Replies 3 ·
Replies
3
Views
10K
Find Eigenvalues & Eigenspace for (3,0) (8,-1) Matrix | Homework Statement
  • · Replies 4 ·
Replies
4
Views
2K
Find Coordinates of Closest Point on y=sqrt(x) to (4,0)
  • · Replies 3 ·
Replies
3
Views
2K
Finding closest point from a parabola to a plane
  • · Replies 3 ·
Replies
3
Views
3K
Finding the focus points of a hyperbola
  • · Replies 3 ·
Replies
3
Views
2K
Find All Elements of Affine Group G(¬) for Hyperbola xy = 1
  • · Replies 7 ·
Replies
7
Views
3K
Find closest possible points between lines? (vectors)? Edit
  • · Replies 2 ·
Replies
2
Views
3K