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!

Mathematics Q

  1. Feb 14, 2005 #1
    Prove that the triangle formed by the asymptotes of the curve with equation x^2 - 2y^2 = 4 and any tangent to the curve is of constant area.

    Thanks. :)
  2. jcsd
  3. Feb 14, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Homework? Well, the answer is do it: find the equations of the asymptotes, and a tangent and voila do it.
  4. Feb 14, 2005 #3
    I'm having problems finding the asymptotes.
  5. Feb 14, 2005 #4
    Could anyone help me do this Q? Thanks.
  6. Feb 14, 2005 #5
    Please could someone show me how to do this Question? I'm having difficulties, because I've barely been taught this chapter and I want to at least see how such a question is answered. Thanks.
  7. Feb 14, 2005 #6
    You have to let us know what u have done?
    Post whatever working u have done(even if its wrong its fine), since that would help us to pitch the answer at the right frequency.

    -- AI
  8. Feb 14, 2005 #7
    I really don't know where to start, I don't know how to find the asymptotes of the curve, that's a key problem...
  9. Feb 14, 2005 #8
    Ok u need to run through the basics a bit then.
    First of all,
    the equation u have is a hyperbola
    Read abt hyperbolas here,

    Asymptotes are mentioned in this article and its also explained how they are obtained.
    I will leave the rest to you for now. Try to go ahead and solve your original problem. If u are getting stuck again, post your working.

    -- AI
  10. Feb 14, 2005 #9


    User Avatar
    Science Advisor
    Homework Helper

    for starters, the asymptotes of xy = 1 seem to be the x and y axes y=0 and x=0, [take derivative of y = 1/x, get -1/x^2, and let x go to infinity, so the slope goes to zero, or let x go to zero, and the slope goes to infinity] so after rotating axes, the asymptotes of uv = (x-y)(x+y) = 1, are probably the lines u=0 and v=0, i.e. x = y and x = -y.

    you might look at this to be sure, as I am allergic this type of thing.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook