The equation of circle o is (x - 2) 2 + (y - 4) 2 = 36. determine which of these points are on the circumference of the circle. there may be more than one correct answer. (2, 4) (8, 4) (-2, 2) (2,-2) (-4, 4) (-2,-2) (6, 6)

To determine position of points with respect to a circle, we need to find the distance of the points to the center of the circle. For an easy way, we could directly insert the points on the option to the equation of the circle. Here's how to analyze the results
(x - 2)² + (y - 4)² = 36 that means the point is located on the circumference of circle
(x - 2)² + (y - 4)² > 36 that means the point is located outside the circumference of circle
(x - 2)² + (y - 4)² < 36 that means the point is located inside the circumference of circle

Check the options one by one
first option (2,4)
(x - 2)² + (y - 4)²
= (2 - 2)² + (4 - 4)²
= 0
0 is less than 36, that means (2,4) is located inside the circumference

second option (8,4)
(x - 2)² + (y - 4)²
= (8 - 2)² + (4 - 4)²
= 6²
6² is equal to 36, that means (8,4) is located on the circumference

third option (-2,2)
(x - 2)² + (y - 4)²
= (-2 - 2)² + (2 - 4)²
= (-4)² + (-2)²
= 16 + 4
= 20
20 is less than 36, that means (-2,2) is located inside the circumference

fourth option (2,-2)
(x - 2)² + (y - 4)²
= (2 - 2)² + (-2 - 4)²
= 0 + (-6)²
= (-6)²
(-6)² is equal to 36, that means (2,-2) is located on the circumference

fifth option (-4,4)
(x - 2)² + (y - 4)²
= (-4 - 2)² + (4 - 4)²
= (-6)²
(-6)² is equal to 36, that means (-4,4) is located on the circumference

sixth option (-2,-2)
(x - 2)² + (y - 4)²
= ( -2 - 2)² + (-2 - 4)²
= (-4)² + (-6)²
= 52
52 is more than 36, that means (-2,-2) is located outside the circumference

seventh option (6,6)
(x - 2)² + (y - 4)²
= (6 - 2)² + (6 - 4)²
= 4² + 2²
= 16 + 4
= 20
20 is less than 36, that means (6,6) is located inside the circumference

ANSWER: (8,4), (2,-2), (-4,4)