Question

what is the center of the circle (x+4)^2+(y-3)^2=4

Answer 1

This is the standard form equation of a circle:
\[(x-h)^2 + (y-k)^2 = r^2\]

Where (h,k) is the center of the circle, and r is the radius. Therefore we can find the (h,k) values from your particular equation to see by inspection what the center will be.

You have:\[ (x+4)^2+(y-3)^2=4\]\[\implies (x- (-4))^2+(y-3)^2=4\]

Therefore h is -4, and k is 3. So your center will be (-4,3)