Question 1092459
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<pre>
{{{x^2 - 4x +y^2 + 4y}}} = 0        Use completing the squares for each group of x- and y-terms separately

{{{(x^2 -4x + 4)}}} + {{{(y^2 + 4y + 4)}}} = {{{4 + 4}}},

{{{(x-2)^2}}} + {{{(y+2)^2}}} = 16.


It is the standard equation of the circle of the radius {{{sqrt(16)}}} = 4, centered at (2,-2).
</pre>

See the lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-a-circle.lesson>Standard equation of a circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/General-equation-of-a-circle.lesson>General equation of a circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Transform-general-eqn-of-a-circle-to-the-standard-form-by-completing-the-squares.lesson>Transform general equation of a circle to the standard form by completing the squares</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-a-circle-given-by-its-general-equation.lesson>Identify elements of a circle given by its general equation</A> 


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>".