1. Limited time only! Sign up for a free 30min personal 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!

Intersection between rotated & translated ellipse and line

  1. Sep 5, 2014 #1
    I have a rotated ellipse, not centered at the origin, defined by x,y,a,b and angle.
    Then I have a segment defined by two points x1,y1 and x2,y2
    Is there a quick way to find the intersection points?

    I used wolfram alpha equation solver, I tried to insert the equation of a line into the one of a standard non rotated, non translated ellipse,


    and resolving for x this is the result


    which is nice.

    Then I took the equation of a rotated and translated ellipse


    and this is the result


    Which is obviously impractical, can anyone suggest a different method?
  2. jcsd
  3. Sep 5, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Do it by hand rather than use the calculator.
    You can either -
    1. Solve for one variable in the line equation and sub into the ellipse equation - solve for the other coordinate ... you know: as usual.

    2. transform the ellipse into standard form, apply the same transformation to the line, find solutions for the transformed system, apply the inverse transformation to the solution.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook