1. Not finding help here? Sign up for a free 30min 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!

Parametric curve, unique pt. P, tangent at P goes through other point.

  1. Oct 28, 2013 #1

    s3a

    User Avatar

    1. The problem statement, all variables and given/known data
    Problem:
    A curve given parametrically by (x, y, z) = (2 + 3t, 2 – 2t^2, -3t – 2t^3). There is a unique point P on the curve with the property that the tangent line at P passes through the point (-10, -22, 76).

    Answer:
    P = (-4, -6, 22)

    What are the coordinates of point P?

    2. Relevant equations
    Derivatives and vector manipulation.

    3. The attempt at a solution
    I read on-line that one must find some vector and that that vector is parallel to the vector of the derivatives with respect to t (so, they're scalar multiples of each other), but I don't know specifically how to start nor do I understand what is going on, so I would greatly appreciate it if someone could tell me what needs to be done to successfully complete this problem and also help me understand what is going on spatially as well.
     
  2. jcsd
  3. Oct 28, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The point P corresponds to some value of t, tP. You can differentiate to find dx/dt, and plugging in t = tP gives you the tangent vector at P. From this, obtain an expression for the tangent line in terms of tP. It remains to plug in the known point that this line passes through.
     
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: Parametric curve, unique pt. P, tangent at P goes through other point.
Loading...