Final answer:
The equations of the asymptotes for the given hyperbola (y-1)^2/9 - (x-2)^2/100 = 1 are y - 1 = ±(3/10)(x - 2) in point-slope form.
Step-by-step explanation:
The question asks for the equations of the asymptotes of the hyperbola (y-1)2/9 - (x-2)2/100 = 1. To find the equations of the asymptotes for a hyperbola in standard form, we use the general equation of the hyperbola (y-k)2/a2 - (x-h)2/b2 = 1, where (h,k) are the coordinates of the center and a and b are the lengths of the semi-major and semi-minor axes, respectively. The asymptotes of this hyperbola can be given as y - k = ±(a/b)(x - h).
In this case, the center of the hyperbola is at (2, 1), a is the square root of 9, which is 3, and b is the square root of 100, which is 10. Therefore, the equations of the asymptotes in point-slope form are y - 1 = ±(3/10)(x - 2).