Deriving Standard Form of Ellipse Equation

[Mahmoud2010]

in the derivation of the standard form of equation of ellipse

[PLAIN]http://img694.imageshack.us/img694/8324/capturedpw.jpg

we squared both sides of equation isn't that means that we have produce we have produced a candidate which doesn't satisfy the original equation.

Thanks

 

[LCKurtz]

There is no problem because all of your steps are reversible. When you work the steps in reverse order, the only place where there is a potential problem is where you take square roots. But if you look carefully, you will see that you are only taking the positive square root of both sides, which themselves are positive numbers. And if you have two positive numbers a and b with a²=b², then a = b. You don't have the possibility that a = ±b.

 

[Mahmoud2010]

I think of this also . but I want to be more certain.

At all Thanks for help.