1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Contour map and Intersection points

  1. Jan 6, 2007 #1
    1. The problem statement, all variables and given/known data

    (i) Drawing a contour map for the function h(x.y) = -12-4x^2+16x-y^2-8y
    (ii) (Continuing from i) at the point (1,-1,7) which direction to move to have
    the maximum increase in height?

    (iii) Find the point closest to the origin on the curve of intersection of the
    plane 2y + 4z = 5 and the cone z^2= 4x^2 + 4y^2.

    2. Relevant equations

    (i) z = -12-4x^2+16x-y^2-8y (then Im stuck)

    (iii) I got f = z <--(not sure if this is right),
    g = 2y +4z = 5
    and h = z^2= 4x^2 + 4y^2.

    then gradient f = lambda * gradient g + mu * gradient h

    3. The attempt at a solution

    then from some caluculation i got two intersection point of (0,5/18,5/9) and (0, 1/10, 1/20) with (0, 1/10, 1/20) the point closest to the origin.
  2. jcsd
  3. Jan 6, 2007 #2


    User Avatar
    Science Advisor

    Do you understand what a "contour map" IS? No, don't set h(x,y)= z. A contour map of a function of two variables is a graph is the xy-coordinates system. Set h(x,y)= equal to a number of different constants and graph each of them. (Looks to me like you will have a number of different hyperbolas with the same asymptotes.)

    Okay, that's the "Lagrange multiplier" method.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Contour Intersection points Date
Find intersections between sphere and parallel tangent planes Jan 9, 2018
Contour Integration Jan 2, 2018
Contour Integration: Branch cuts Oct 28, 2017
Contour Integrals: Working Check Oct 21, 2017