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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-> 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)
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.
The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".
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https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
