Answer: The point that satisfies the equation is E. (-3, -4).
Explanation:
To determine which point lies on the circle represented by the equation (x − 3)² + (y + 4)² = 6², we can substitute the coordinates of each point into the equation and see which one satisfies the equation.
A. (9, -2): (9 − 3)² + (-2 + 4)² = 6²
(6)² + (2)² = 36
36 + 4 = 40 ≠ 36
B. (0, 11): (0 − 3)² + (11 + 4)² = 6²
(-3)² + (15)² = 36
9 + 225 = 234 ≠ 36
C. (3, 10): (3 − 3)² + (10 + 4)² = 6²
(0)² + (14)² = 36
0 + 196 = 196 ≠ 36
D. (-9, 4): (-9 − 3)² + (4 + 4)² = 6²
(-12)² + (8)² = 36
144 + 64 = 208 ≠ 36
E. (-3, -4): (-3 − 3)² + (-4 + 4)² = 6²
(-6)² + (0)² = 36
36 + 0 = 36
The point that satisfies the equation is E. (-3, -4).