Which of the following describes the relationship between the circle (x - 2)^2 + (y + 1)^2 = 9 and the point (5, 0)?
Correct: B
The equation of the circle is (x - 2)^2 + (y + 1)^2 = 9. This means the center of the circle is (2, -1) and the radius squared is r^2 = 9, so r = 3.
To determine the relationship of the point (5, 0) to the circle, we calculate the distance from the center (2, -1) to the point (5, 0).
Distance d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((5 - 2)^2 + (0 - (-1))^2)
d = sqrt((3)^2 + (1)^2)
d = sqrt(9 + 1)
d = sqrt(10)
Now, compare this distance to the radius (r = 3).
Since sqrt(10) is approximately 3.16, and 3.16 > 3, the distance from the center to the point is greater than the radius. Therefore, the point (5, 0) is outside the circle.