SOLUTION: The circle with the equation x^2 − 2x + y^2 + 6y = 6 has centre C and radius r, where 1. C = (1, −3) ; r = 4 2. C = (1, −3) ; r = 16 3. C = (−1, 3) ; r = 4 4. C

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Question 1142454: The circle with the equation
x^2 − 2x + y^2 + 6y = 6
has centre C and radius r, where
1. C = (1, −3) ; r = 4
2. C = (1, −3) ; r = 16
3. C = (−1, 3) ; r = 4
4. C = (−1, 3) ; r = 16
5. C = (0, 0) ; r = sqrt(6)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
duplicate.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Apply the standard procedure completing the squares for x- and y- terms separately to transform 

the given general equation of the circle into its standard form.


    x^2 − 2x + y^2 + 6y = 6


    (x^2 - 2x + 1) + (y^2 + 6y + 9) = 6 + 1 + 9


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


    (x - 1)^2 + (y + 3)^2 = 4^2


The circle has the center at the point (1,-3) and the radius of 4.


ANSWER.  The answer is #1.


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If you want to learn more about this procedure and associated notions, look into the lessons
    - Standard equation of a circle
    - General equation of a circle
    - Transform general equation of a circle to the standard form by completing the squares
    - Identify elements of a circle given by its general equation
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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