The equation for the circle is given by:
[tex]\left(x-h\right)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r represents the radius.
Now, if we look at the given equation:
[tex]\left(x-2\right)^2+(y+4)^2=36[/tex]
For h:
h = 2
For k:
k=-4
for r:
r²=36
r=√36
r =6
Hence, the center is (2,-4) and the radius is 6.
The correct answer is option b.
