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Given the general equation of a circumference, we use the perfect square trinomial factorization process to transform it into the reduced equation, and thus determine the center and radius of the circumference. To do so, the general equation must meet two conditions:

the coefficients of the terms x

^{2}and y^{2}must be equal to 1;there should not be the term xy.

So let's determine the center and radius of the circle whose general equation is x^{2} + y^{2} - 6x + 2y - 6 = 0. Looking at the equation, we see that it meets both conditions. Like this:

Step 1: We group the terms into

**x**and the terms in**y**and we isolate the term independent

x^{2} - 6x + _ + y^{2} + 2y + _ = 6

Step 2: We determine the terms that complete the perfect squares in the variables.

**x**and**y**, adding to both members the corresponding installments

Step 3: We factor in the perfect square trinomials

(x - 3) ^{2} + (y + 1) ^{2} = 16

4th step: obtained the reduced equation, we determine the center and the radius