Final answer:
The center of the ellipse given by the equation (x-5)^2 /36+(y+2)^2/9=1 is the point (5, -2).
Step-by-step explanation:
The question asks for the center of the ellipse represented by the equation (x−5)2 /36+(y+2)2/9=1. The standard form for the equation of an ellipse is (x-h)2/a2 + (y-k)2/b2 = 1, where (h, k) is the center of the ellipse.
Comparing this to the given equation, we can deduce that the ellipse's center is at the point (5, -2).