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Finding the tangent plane and normal line

  1. Mar 26, 2012 #1
    D is a set of all points (x,y) in R2 distinct from (0,0).
    I have the funtion f: D --> R which is defined by:
    f(x,y) = (2xy)/(x2+y2

    Im asked to find the equations (in plural) of the tangelnt plane and the normal line to the graph of the function at (1,2)

    My attempt:

    I use the tangent plane z= f(a,b)+f1(a,b)*(x-a) + f2(a,b)*(y-b)

    f(1,2) = 4/5
    f1(1,2) = 12/25
    f2(1,2) = -6/25

    when I put that into the tangent plane equation and simplify I get: (12/25)x - (6/25)y+4/5

    Is this my normal line?

    Im very confused, because the assigment asks me to find multiple equations of the tangent plane which I have never done before.

    Help is appreciated.
     
  2. jcsd
  3. Mar 26, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

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    Before, you had "z= " that. And what happened to the "- a" and "- b"?

    You just said it was the "tangent plane equation". A plane is not a line!

    Any equation can be written in a number of ways. For example, multiplying both sides by a constant will give a new equation for the same object. Or just move terms from one side to another.
     
  4. Mar 27, 2012 #3
    So if I do like this:

    z*2 = ((12/25)x - (6/25)y+4/5) * 2

    it can be concidered a valid answer?
     
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