1. Limited time only! Sign up for a free 30min personal 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!

Tangent plane equation question.

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a surface ω with equation:

    [tex]x^2 + y^2 + 4z^2 = 16[/tex]

    Find an equation for the tangent plane to ω at point (a,b,c).

    2. Relevant equations

    Tangent plane, 3 variables:

    [tex]f_{1}(a,b,c)(x-a) + f_{2}(a,b,c)(y-b) + f_{3}(a,b,c)(z-c)= 0[/tex]

    3. The attempt at a solution

    I get at the end:

    [tex]ax + by + 4cz = a^2 + b^2 + 4c^2[/tex]

    The textbook gives me:

    [tex]ax + by + 4cz = a^2 + b^2 + 4c^2 = 16[/tex]

    Where does the 16 come from?

    Comparing to this problem, as an example:

    Find an equation of the tangent plane to the sphere [tex]x^2 + y^2 + z^2 = 6 [/tex] at point (1,-1,2). This on is simple. But not the first above.

    And is it possible to solve this by expanding to a fourth variable, such as ω?
     
  2. jcsd
  3. Apr 15, 2013 #2
    The (a, b, c) point must satisfy the equation of the surface, hence the right-hand side equals 16.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Tangent plane equation question.
Loading...