Final answer:
The center of the circle is at (0, 1), and the radius of the circle is 9 units.
Step-by-step explanation:
To find the radius and center of the circle represented by the equation x²+(y-1)²=81, we can compare this equation to the standard form of a circle's equation, which is (x-h)²+(y-k)²=r², where (h,k) is the center of the circle and r is the radius.
Looking at the given equation, we can see that h=0 and k=1, which means the center of the circle is at (0,1). The radius can be found by taking the square root of 81, which gives us r=9. Therefore, the radius of the circle is 9 units.