Final answer:
By comparing the distances from the origin to the point (0, 4) and (-1, 5), we find that they are not the same, so the point (-1, 5) does not lie on the circle. The correct answer is b. No.
Step-by-step explanation:
To determine if the point (-1, 5) lies on the circle centered at the origin and contains the point (0, 4), we need to check if the distance from the origin to both points is the same. The distance of a point (x, y) from the origin (0, 0) is given by the equation √(x² + y²). For the point (0, 4), the distance is √(0² + 4²) = 4.
Now, we calculate the distance for the point (-1, 5) to see if it also equals 4: √((-1)² + 5²) = √(1 + 25) = √26. Since √26 is not equal to 4, the point (-1, 5) does not lie on the circle. Therefore, the correct answer is b. No.