1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Parallel Tangent Planes

  1. Mar 4, 2006 #1
    "Find the points on the surface 4x^2+5y^2+5z^2=1 at which the tangent plane is parallel to the plane 4x-37-1z=-2"

    Im very lost when it comes to this problem. I know that if the planes are parallel, the normal vectors will be parallel. So I think I need to multiply plane (4x-37-1z=-2)'s normal vector by some consistent?

    Im not really sure what to do, nor do I understand the concept. Any help would be appreciated. :frown:
  2. jcsd
  3. Mar 4, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Back again? As I said in an earlier post, Let [itex]F(x,y,z)= 4x^2+5y^2+5z^2[/itex] so that you can think of the surface as a "level surface for F: F(x,y,z)= 1. Then the gradient of F, [itex]\nabla F= 8x i+ 10y j+ 10z k[/itex] is normal to the surface. You need to find (x, y, z) that not only satisfy [itex]4x^2+5y^2+5z^2= 1[/itex] but so that
    8x i+ 10y j+ 10z k is a multiple of 4i+ 3j- k (I assume that when you typed "37" you meant "3y")- that is, 8x= 4a, 10y= 3a, 10z= -a for some (x,y,z) and a with (x,y,z) satisfying [itex]4x^2+5y^2+5z^2= 1[/itex]. Solve 8x= 4a for x, 10y= 3a for y, 10z= -a for z and substitute into the equation of the surface to get an equation in a.
    Last edited: Mar 4, 2006
  4. Mar 4, 2006 #3
    Awsome, great instructions.

    I was doing nearly all of that, but I had a transcription error similar to my typo. :rofl: Also I wasnt sure where to plug "a" into, but you simply plug it into the 8x=4a eqns etc. Really helped, thx alot :cool:

    actually i posted this first. im gonna look over that other thread after work
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?