Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$
1 answer:
Answer:
16π ≈ 50.27 square units
Step-by-step explanation:
The equation is that of a circle of radius 4. The area of a circle is given by ...
A = πr²
A = π(4²) = 16π ≈ 50.27 . . . . square units
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The equation can be put into the standard form for a circle to find its radius.
(x^2 -2x) +(y^2 +6y) = 6 . . . . collect variable terms on the left
(x^2 -2x +1) +(y^2 +6y +9) = 6 + 1 + 9 = 16 . . . . . complete the squares
(x -1)^2 +(y +3)^2 = 4^2 . . . . . the radius is 4
Compare to the form ...
(x -h)^2 +(y -k)^2 = r^2 . . . . circle of radius r centered at (h, k)
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