Question 45671
x^2+y^2-4x+8y=4

Rearrange and complete the square on the x and the y terms, as follows:

x^2-4x+4 + y^2+8x+16 = 4 + 4 + 16
Factor as follows:

(x-2)^2 + (y+4)^2 = 24

Center is at (2,-4)
radius is sqrt24 = 2sqrt6

Cheers,
Stan H.