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!

Homework Help: Elimination math problem

  1. Sep 21, 2007 #1
    1. The problem statement, all variables and given/known data

    If x=2at/(1+t^2) and y=b(1-t^2)/(1+t^2), show that x^2/a^2+y^2/b^2=1

    3. The attempt at a solution

    I've tried squaring both equations: xt^2=4a^2t^2/(1+2t^2+t^4)


    Now I've tried adding x^2 and y^2: 4a^2t^2+b^2(1-2t^2+t^4)/(1+2t^2+t^4)

    Am I able to cancel any of this down now?
  2. jcsd
  3. Sep 21, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Try solving the y equation for t and substituting that t into the x equation.
  4. Sep 21, 2007 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I think you'll find it easier if you add x2/a2 to y2/b2.

    Its made fairly easy since the denominators are the same and thus its just a manipulation of the numerator.
  5. Sep 21, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    First simplify each term x^2/a^2 and y^2/b^2.

    Then expand the numerator of y^2/b^2. Add it to x^2/a^2, which has the identical denominator.

    Can you get the rest?
    Last edited: Sep 21, 2007
  6. Sep 22, 2007 #5
    Oh yes thanks! x^2/a^2+y^2/b^2=4t^2+1-2t^2+t^4/1+2t^2+t^4
    So the left hand side cancels to give 1.
    Thanks again!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Elimination math problem
Two pencils of planes have a common plane