Final answer:
The foci of the hyperbola (y-4)²/25 - (x-2)²/11 = 1 are at (2, 10) and (2, -2), which is not listed among the provided options.
Step-by-step explanation:
The equation given for the hyperbola is (y-4)²/25 - (x-2)²/11 = 1. This is the standard form of a hyperbola centered at (h, k), with a vertical transverse axis. The general form is (y-k)²/a² - (x-h)²/b² = 1.
For the given hyperbola, h = 2, k = 4, a² = 25, and b² = 11. The distance of the foci from the center along the transverse axis is c, where c² = a² + b². Substituting the given values, we get c² = 25 + 11 = 36, hence, c = √36 = 6.
Since the hyperbola is vertical, the foci are above and below the center. So, the foci are at (2, 4 ± 6), which simplifies to (2, 10) and (2, -2).
None of the options provided in the question are correct. The correct foci of the hyperbola are at (2, 10) and (2, -2).