The easiest way is to try the point (-4,1), that is, x=-4, y=1, to see which equation works. b works.
The usual way to do it is to find the equation of the circle standard form of a circle is (x-h)²+(y-k)²=r², (h,k) are the coordinates of the center, r is the radius. in this case, the center is (-2,1), so (x+2)²+(y-1)²=r² the given point (-4,1) is for you to find r: (-4+2)²+(1-1)²=r², r=2 so the equation is (x+2)²+(y-1)²=2² expand it: x²+4x+4+y²-2y+1=4 x²+y²+4x-2y+1=0, which is answer b.
