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Tangent line equation

  1. Oct 19, 2009 #1
    1. The problem statement, all variables and given/known data
    The ellipsoid 4x^2 + 2y^2 + z^2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2)


    2. Relevant equations
    x = x0 + at
    y = y0 + bt
    z = z0 + ct

    3. The attempt at a solution
    Well i know that x0,y0 and z0 are given by the point(1,2,2) and that's pretty much it. I dont know how to use the information given in the first part of the question.
    I put y=2 in the ellipsoid equation and got 4x^2 + z^2 = 8. Now what?
     
    Last edited: Oct 19, 2009
  2. jcsd
  3. Oct 20, 2009 #2

    HallsofIvy

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    Great! Now find a tangent line to that ellipse at x= 1, z= 2. What that will give you will probably be something line z= ax+ b. Okay, let x= t, the parameter. x= t, z= at+ b and, of course, y= 2.
     
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