Final answer:
The foci of the hyperbola are (-1 + 2√13, 6) and (-1 - 2√13, 6).
Step-by-step explanation:
To find the foci of the hyperbola, we need to first identify the values of a and b in the equation (y-6)²/36 - (x+1)²/16 = 1, where (h, k) is the center of the hyperbola.
In this case, h = -1 and k = 6.
The value of a is the square root of the denominator of the y term, so a = √36 = 6.
The value of b is the square root of the denominator of the x term, so b = √16 = 4.
The coordinates of the foci can be found using the formula c = √(a² + b²), where c is the distance from the center of the hyperbola to the foci.
Plugging in the values, we get c = √(6² + 4²) = √(36 + 16) = √52 = 2√13.
Therefore, the foci of the hyperbola are (-1 + 2√13, 6) and (-1 - 2√13, 6).