Question

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$

Answer 1

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

_____

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)