Results 1 to 2 of 2

Math Help - Prove this!!!!

  1. #1
    Banned
    Joined
    Dec 2008
    Posts
    67

    Prove this!!!!

    If e and e' are the eccentricity of a hyperbola and its conjugate, prove that
    \left(\frac{1}{e^2}\right)+\left(\frac{1}{e'^2}\ri  ght)=1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member teuthid's Avatar
    Joined
    Feb 2008
    From
    Bowling Green, OH
    Posts
    49

    Ugly Algebra Proof

    e=\frac{\sqrt{a^2+b^2}}{a}

    \rightarrow e'=\frac{\sqrt{b^2+a^2}}{b}

    \rightarrow \left( \frac{1}{e^2} \right) + \left( \frac{1}{{e'}^2} \right) = {\left( \frac{1}{\frac{\sqrt{a^2+b^2}}{a}} \right)}^2 + {\left( \frac{1}{\frac{\sqrt{b^2+a^2}}{b}} \right)}^2

    ={\left( \frac{a}{\sqrt{a^2+b^2}} \right)}^2 + {\left( \frac{b}{\sqrt{b^2+a^2}} \right)}^2

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

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 05:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 09:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 05:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum