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## Main Question or Discussion Point

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).

[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).