Completing the square involving square roots

[Monsterman222]

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:

$$\sqrt{\left(x -c\right)^{2} +y^{2}}-\sqrt{\left(x+c\right)^{2}+y^{2}} = 2a$$

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

$$x^{2}\left(c^{2}-a^{2}\right)-a^{2}y^{2}=a^{2}\left(c^{2}-a^{2}\right)$$

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).

 

[tiny-tim]

Hi Monsterman222!

It's wrong …

it's not completing the square, it's just squaring both sides (after rearranging), twice

 

[ardie]

you do have to complete the square eventually, just do square both sides frist

 

[Monsterman222]

Awesome, thanks! I was able to get it without completing the square, just squaring twice qfter rearranging.