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Aus Online Mathematik Brückenkurs 1

As the equation stands, it is difficult directly to know anything about the circle, but if we complete the square and combine x- and y-terms together in their own respective square terms, then we will have the equation in the standard form

(x−a)2+(y−b)2=r2

and we will then be able to read off the circle's centre and radius.

If we take the x- and y-terms on the left-hand side and complete the square, we get

x2+2xy2−2y=(x+1)2−12=(y−1)2−12

and then the whole equation can be written as

(x+1)2−12+(y−1)2−12=1

or, with the constants moved to the right-hand side,

(x+1)2+(y−1)2=3.

This is a circle having its centre at (-1,1) and radius 3 .