Results 1 to 1 of 1

Math Help - Equations for the tangent line to the curve

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    144

    Question Equations for the tangent line to the curve

    Find equations for the tangent line to the curve

    xyz + z^{3} = 24, x^{3}y^{2}z + y^{3} = 4x - 2

    at the point (1,-1,3)

    Okay, if I can find parametric equations representing this curve I can easily find a tangent vector along the curve at the point (1,-1,3) by simply differentiating my parametric equations.

    At this point I'll have a tangent vector along the curve, I want a tangent line to the curve at the point (1,-1,3), so I'll simply define a new line that points in the direction of my tangent vector, starting at the point (1,-1,3).

    Problem is, I can't seem to find a reasonable way of finding parametric equations for the curve.

    Any ideas?

    EDIT: I've solved it by taking the gradient of both functions F(x,y,z) = 0 and G(x,y,z) = 0 evaluated at the point (1,-1,3) and taking the cross product between to produce my vector along the tangent line.
    Last edited by jegues; October 30th 2010 at 09:59 AM. Reason: SOLVED
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Tangent line to a curve.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 19th 2011, 06:53 AM
  2. Replies: 5
    Last Post: November 4th 2009, 06:49 PM
  3. Tangent line to curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 14th 2009, 04:43 PM
  4. Tangent line to a given curve.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 2nd 2009, 07:38 AM
  5. Tangent line to the curve
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 1st 2009, 10:16 AM

/mathhelpforum @mathhelpforum