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: Tangent plane.

  1. Feb 5, 2008 #1
    Please,help me with this problem.
    1. The problem statement, all variables and given/known data
    Prove that the two families of parabolas
    [tex]y^2=4a(a-x),a>0[/tex] and [tex]y^2=4b(b+x),b>0[/tex]
    form an orthogonal net. Specifically, check that for any a, b > 0 these two parabolas
    are perpendicular to each other at the points where they intersect.

    3. The attempt at a solution

    Their tangent spaces at point [tex](x_0,y_0)[/tex] are



    If they are perpendicular then we have

    [tex]4y_0^2-16ab=0\Rightarrow y_0^2=4ab[/tex]

    from the equations of parabolas we have



    if we substitute [tex]x_0[/tex]

    So they are perpendicular.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted