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!

Finding the unit vector for an ellipse

  1. Dec 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Given the ellipse
    ##0.084x^2 − 0.079xy + 0.107y^2 = 1 ##
    Find the semi-major and semi-minor axes of this ellipse, and a unit vector in the
    direction of each axis.

    I have calculated the semi-major and minor axes, I am just stuck on the final part.
    2. Relevant equations
    this is where ##ux^2+2vxy+wy^2=1##
    3. The attempt at a solution
    I have calculated the two eigenvalues, 0.13664... and 0.05436... and therefore found the semi-major and semi-minor axes. I'm just not sure where to go next. I have worked out the ratios for q/p but I'm not sure how to use them.
  2. jcsd
  3. Dec 9, 2014 #2


    Staff: Mentor

    What did you get for the semi-major and semi-minor axes? If you found the angle ##\alpha## that one of them makes with the x-axis, the vector ##<cos(\alpha), sin(\alpha)>## is a unit vector in the direction of one of these axes. ##<-sin(\alpha), cos(\alpha)>## is a unit vector in the other one's direction.
  4. Dec 9, 2014 #3
    I got 2.705 for the semi-minor and 4.2890 for the semi-major. As far as I was aware these were just lengths, I solved them by equating those two q/p equations and rearranging to give ##λ^2-(u+w)λ+uw-v^2=0## and solving.
    I basically followed the steps on these notes http://quince.leeds.ac.uk/~phyjkp/Files/Teach/phys2370notes4.pdf [Broken] (It's page 2 on there) but I'm really confused about that last part (9.88)
    Last edited by a moderator: May 7, 2017
  5. Dec 9, 2014 #4


    Staff: Mentor

    If you have u and v, you can use either eigenvalue and equation 9.85 to find the ratio q/p. Then the coordinates of a direction vector are (p, q).
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: Finding the unit vector for an ellipse
  1. Finding a unit vector. (Replies: 2)

  2. Finding unit vector (Replies: 6)