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!

Hyperbola question

Tags:
  1. Jun 4, 2015 #1
    Back in 10th degree, I have learned that in Clapeyron-Mendeleev coordinates ( eq: p-V) , an Isotherm transformation of an ideal gas ( with constant mass throughout the transformation ) is represented with an arc of an hyperbola. Now, I have learned that hyperbola equation is : x2 / a2 - y2/b2 = 1 ( or written in the other way, with y2 as first term ) . This equation , plotted, result in a different type of graphic as I learned on T=constant transformation ! My question is why I used to draw the curbe line graph in p-V coordinates of an equation like y=1/x ? ( as pV= constant ) , saying that it is a hyperbola? What has got to do with an arc of hyperbola? Thank you !
     
  2. jcsd
  3. Jun 4, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    If you have the curve given by ## x^2 - y^2 = 1## and you rotate it 45 degrees around the origin, what do you get?
     
  4. Jun 4, 2015 #3

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    As a variant of DEvens's post, suppose you define u=x+y and v=x-y. What is the curve in terms of u and v?
     
  5. Jun 5, 2015 #4
    Thank you for your responses !
    @DEvens :yes, I realised that x^2−y^2=1 shifted by π/4 radians results in my desired part of graph, but... something is not clear in my mind. How can I assume that I can rotate the graph and still get something mathematically valid? There's something not clear in my mind...
    @robphy : in terms of u and v, u*v = x^2-y^2 =constant =1 , as in a normal isotherm. But from the (x,y) coordinates , I can define a new system of coordinates, given by (x+y, x-y ) ? Just like when I shift by π/4 radians the normal hyperbola graph?
     
  6. Jun 5, 2015 #5

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    A hyperbola is shape, not a function.
    Focus on the curve, and forget about the axes.

    Drawn on a piece of paper, that curve is a hyperbola... no matter how you slide, reflect, or rotate the piece of paper.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hyperbola question
  1. Hyperbola question (Replies: 3)

  2. Hyperbola equation (Replies: 4)

  3. The hyperbola (Replies: 6)

Loading...