Which circle does the point (-1, 1) lie on?(x-5)2 + (y+2)2 = 25(x-2)2 + (y+6)2 = 25(x-2)2 + (y-5)2 = 25(x-2)2 + (y-2)2 = 25

To determine which circle the point (-1, 1) lies on, we need to substitute the x and y coordinates of the point into the equations of the circles and see which one(s) hold true.

1. For the first circle, (x-5)² + (y+2)² = 25, substituting x = -1 and y = 1, we get: ((-1)-5)² + ((1)+2)² = 25 (-6)² + (3)² = 25 36 + 9 = 45, which is not equal to 25. So, the point does not lie on this circle.

2. For the second circle, (x-2)² + (y+6)² = 25, substituting x = -1 and y = 1, we get: ((-1)-2)² + ((1)+6)² = 25 (-3)² + (7)² = 25 9 + 49 = 58, which is not equal to 25. So, the point does not lie on this circle.

3. For the third circle, (x-2)² + (y-5)² = 25, substituting x = -1 and y = 1, we get: ((-1)-2)² + ((1)-5)² = 25 (-3)² + (-4)² = 25 9 + 16 = 25, which is equal to 25. So, the point lies on this circle.

4. For the fourth circle, (x-2)² + (y-2)² = 25, substituting x = -1 and y = 1, we get: ((-1)-2)² + ((1)-2)² = 25 (-3)² + (-1)² = 25 9 + 1 = 10, which is not equal to 25. So, the point does not lie on this circle.

Therefore, the point (-1, 1) lies on the third circle, (x-2)² + (y-5)² = 25.