Solving Lagrange Problem Near (9,12,5)

  • Thread starter Thread starter navalstudent
  • Start date Start date
  • Tags Tags
    Lagrange
Click For Summary
SUMMARY

The discussion centers on solving the Lagrange problem of finding the point on the cone defined by the equation z² = x² + y² that is closest to the point (9, 12, 5). The user has derived the equations z² = x² + y², x = (9/12)y, and -2xz + 9z + 5x = 0. Participants confirm that the user is on the right track and suggest using substitution to simplify the equations further.

PREREQUISITES
  • Understanding of Lagrange multipliers in optimization
  • Familiarity with conic sections and their equations
  • Basic algebraic manipulation skills
  • Knowledge of multivariable calculus concepts
NEXT STEPS
  • Study the method of Lagrange multipliers in depth
  • Learn about conic sections and their geometric properties
  • Practice algebraic substitution techniques for solving systems of equations
  • Explore optimization problems involving constraints in multivariable calculus
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on optimization, calculus, and geometric analysis.

navalstudent
Messages
6
Reaction score
0
Hi, I am supposed to find the point on the cone z^2=x^2+y^2 which is closest to the point(9,12,5).

here is my work:

http://img27.imageshack.us/my.php?image=lagrange001.jpg

Is it correct so far?

If it is: I get stuck when trying to solve the equations z^2=x^2+y^2, x=9/12*y, and -2xz+9z+5x=0. Can someone please give me some advice?
 
Physics news on Phys.org
It looks to me like you are on the right track. Now use the second equation to eliminate x or y. It will work. Just keep going.
 

Similar threads

Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Can't get Lagrange multiplier to work in a single exercise
  • · Replies 16 ·
Replies
16
Views
3K
How should I solve this Diophantine equation word problem?
  • · Replies 4 ·
Replies
4
Views
2K
Center of mass of spherical shell inside of cone (Apostol Problem).
  • · Replies 3 ·
Replies
3
Views
2K
Find the curve with the shortest path on a surface (geodesic)
  • · Replies 3 ·
Replies
3
Views
3K
Calculation regarding to Lagrange Multiplier
  • · Replies 5 ·
Replies
5
Views
3K
Maximizing volume of a box without lagrange multipliers
  • · Replies 5 ·
Replies
5
Views
5K
Lagrange multiplier systems of equations -- Help please
  • · Replies 13 ·
Replies
13
Views
2K
How Do You Solve Lagrange Multipliers with Complex Constraints?
  • · Replies 8 ·
Replies
8
Views
2K
How to Solve LaGrange Multiplier Problems for Intersection of Surfaces?
  • · Replies 5 ·
Replies
5
Views
2K