Question 1046374
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ +\ 4x\ -\ 2y\ =\ -1]


Rearrange:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ +\ y^2\ -\ 2y\ =\ -1]


Complete the square on x


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ +\ 4\ +\ y^2\ -\ 2y\ =\ -1\ +\ 4]


Complete the square on y


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ +\ 4\ +\ y^2\ -\ 2y\ +\ 1\ =\ -1\ +\ 4\ +\ 1]


Collect the constant terms in the RHS


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ +\ 4\ +\ y^2\ -\ 2y\ +\ 1\ =\ 4]


The Right Hand Side is now the Radius SQUARED.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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