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Completing the square involving square roots

  1. Jun 26, 2011 #1
    Hi, I was looking at the derivation of the equation for a hyperbola on Wolfram Mathworld. In one step, the webpage instructs you to "complete the square". It starts with:

    [tex]\sqrt{\left(x -c\right)^{2} +y^{2}}-\sqrt{\left(x+c\right)^{2}+y^{2}} = 2a[/tex]

    and then says, "rearranging and completing the square gives":

    [tex]x^{2}\left(c^{2}-a^{2}\right)-a^{2}y^{2}=a^{2}\left(c^{2}-a^{2}\right)[/tex]

    How did he do this? The original page can be found at http://mathworld.wolfram.com/Hyperbola.html and it's equations (3) and (4).
     
  2. jcsd
  3. Jun 26, 2011 #2

    tiny-tim

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    Hi Monsterman222! :smile:

    It's wrong :rolleyes:

    it's not completing the square, it's just squaring both sides (after rearranging), twice :wink:
     
  4. Jun 27, 2011 #3
    you do have to complete the square eventually, just do square both sides frist
     
  5. Jun 27, 2011 #4
    Awesome, thanks! I was able to get it without completing the square, just squaring twice qfter rearranging.
     
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