Results 1 to 2 of 2

Math Help - Arc Length Parametrisation

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    UK
    Posts
    11

    Arc Length Parametrisation

    Hi all,

    I need to find the arc length parametrisation of alpha = ( (1-t^2)/(1+t^2) , (2t)/(1+t^2) )

    So first of all I differentiated to find alpha' = ( (-4t) / (1+t^2)^2 , (2-2t^2) / (1+t^2)^2 )

    and then tried sqrt(x^2 + y^2) but didn't get anything near what the answer is supposed to be ( |alpha'| = 2 / 1 + t^2 )

    Please help!!

    Many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,040
    Thanks
    885

    Re: Arc Length Parametrisation

    review your algebra ...

    \sqrt{\left(\frac{-4t}{(1+t^2)^2}\right)^2 + \left(\frac{2-2t^2}{(1+t^2)^2}\right)^2}

    \sqrt{\frac{16t^2}{(1+t^2)^4} + \frac{4-8t^2+4t^4}{(1+t^2)^4}}

    \sqrt{\frac{4t^4+8t^2+4}{(1+t^2)^4}}

    \sqrt{\frac{4(t^4+2t^2+1)}{(1+t^2)^4}}

    \sqrt{\frac{4(t^2+1)^2}{(1+t^2)^4}}

    \sqrt{\frac{4}{(1+t^2)^2}}

    \frac{2}{1+t^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Arc Length and Chord Length
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 22nd 2010, 02:24 AM
  2. parametrisation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2010, 02:19 AM
  3. Length needed from a known length and angle
    Posted in the Geometry Forum
    Replies: 4
    Last Post: July 21st 2009, 07:17 AM
  4. arc length and parameterized curve length
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2008, 03:33 AM
  5. Arc length and chord length
    Posted in the Geometry Forum
    Replies: 8
    Last Post: December 19th 2007, 04:20 PM

Search Tags


/mathhelpforum @mathhelpforum