Question

find center & radius for the following x^2+(y+5)^2=81

Answer 1

just compare the general equation of circle :
(x-h)^2 + (y-k)^2 = r^2
with h,k is the center of circle, r its radius

Answer 2

If you don't remember the formula, you could work out the answer this way:

set x = 0, solve for the values of y (call them \(y_1, y_2\))
set y = 0, solve for the values of x (call them \(x_1,x_2\))

The center of the circle will be at \((\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2))\)
The radius of the circle will be \(|\frac{1}{2}(x_1-x_2)|\) or \(|\frac{1}{2}(y_1-y_2)|\)

By setting x and y = 0 and solving, you're finding the 4 compass points of the circle.