Answer:
6π ≈ 18.850
Explanation:
A vertical line through the center of the circle will contain the diameter. For x = -2, the values of y will be at opposite ends of the diameter.
... (-2)² + y² + 4(-2-y) -1 = 0 . . . . use -2 for x
... y² -4y -5 = 0 . . . . . . . . . . . . . . simplify
... (y -5)(y +1) = 0 . . . . . . . . . . . . . factor
... y = -1 or 5 . . . . . . . . . . . . . . . . the product is zero when a factor is zero
These values are separated by 5 -(-1) = 6, so the diameter is length 6. The circumference is π times that value:
... circumference = 6π ≈ 18.8496