Results 1 to 2 of 2

Math Help - points on the surface

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    129

    points on the surface

    Find the points on the surface at which the tangent plane is parallel to the plane .
    How do I get started?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by zpwnchen View Post
    How do I get started?

    Find the points on the surface at which the tangent plane is parallel to the plane .
    Parallel planes have the same normal vector (i.e. \langle 3,3,-1\rangle). The constant term is irrelevant.

    The equation for the tangent plane is

    F_x(x_0,y_0,z_0)(x-x_0)+F_y(x_0,y_0,z_0)(y-y_0)+F_z(x_0,y_0,z_0)(z-z_0)=0

    F_x=2x
    F_y=6y
    F_z=8z

    So you want 2x_0=3k, 6y_0=3k, and 8z_0=-k (because you have to take into account the normal vector can be scaled by any constant k).

    Spoiler:
    So the points are \left(\frac{3k}{2},\frac{k}{2},-\frac{k}{8}\right).

    Now you need to solve for k given the initial equation:

    \frac{9k^2}{4}+3\frac{k^2}{4}+4\frac{k^2}{64}=1 \implies k=\pm\frac{4}{7}

    So the two points are:

    \left(\frac{6}{7},\frac{2}{7},-\frac{1}{14}\right) and \left(-\frac{6}{7},-\frac{2}{7},\frac{1}{14}\right)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Points on a surface and differentiability.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 17th 2009, 08:11 PM
  2. Stationary points for surface
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 15th 2009, 04:16 AM
  3. Find the points on the surface
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 16th 2009, 04:06 PM
  4. Find the points on the surface
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 3rd 2008, 05:23 PM
  5. Replies: 3
    Last Post: May 5th 2006, 10:22 AM

Search Tags


/mathhelpforum @mathhelpforum