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Curve and tangent of a surface intersected by a plane

  1. Oct 7, 2009 #1

    Ral

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    1. The problem statement, all variables and given/known data
    a.)[tex]\sqrt{x^2+y^2}[/tex]
    Find the equation of the tangent plane at the point given by: x = 1, y = 1
    Draw the 3d-graph of the surface and the tangent plane.
    [tex]\stackrel{\rightarrow}{n}[/tex] = the normal vector to the tangent plane.

    b.) If the surface is intersected with the plane y = 1, what curve do you get?
    Find the intersection of the tangent line to the resulting curve when x = 1.
    Draw a 2d graph of the curve and the tangent line.

    c.) Is the tangent line obtained in part (b) orthogonal to [tex]\stackrel{\rightarrow}{n}[/tex]?


    2. Relevant equations



    3. The attempt at a solution
    I have part a done.

    For the tangent plane, I have:
    [tex]z= \frac{2}{\sqrt{2}}(x-1)+\frac{2}{\sqrt{2}}(y-1)+\sqrt{2}[/tex]

    and [tex]\stackrel{\rightarrow}{n}=(\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},-1)[/tex]

    I'm not quite sure what to do for part b. I was also trying to use Maple to do the 3d graph, but that was also confusing me, if possible, can I also see what it's suppose to look like.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 7, 2009 #2

    Mark44

    Staff: Mentor

    Is your surface [tex]z = \sqrt{x^2 + y^2}[/tex]?
    You didn't state that in your post. Part b asks you to find the curve where the plane y = 1 intersects your surface. Just substitute y = 1 in the equation of your surface. What do you get?
     
  4. Oct 7, 2009 #3

    Ral

    User Avatar

    Yeah, [tex]z = \sqrt{x^2 + y^2}[/tex] is the surface.

    So the curve would then be [tex]\sqrt{x^2 + 1}[/tex]?
     
  5. Oct 7, 2009 #4

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    That isn't an equation; it's just an expression. What goes on the other side of the = sign?

    Once you answer that, put it in a form you can recognize and identify it.
     
  6. Oct 8, 2009 #5

    Ral

    User Avatar

    [tex]
    z = \sqrt{x^2 + 1}
    [/tex]

    Then would that be the curve?
     
  7. Oct 8, 2009 #6

    Mark44

    Staff: Mentor

    That would be the equation of the curve, which is what the problem is really asking for.
     
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