The general equation for a circle is as follows

where (h,k) represents the coordinates of the center of the circle and r is its radius.
Knowing this, we simply identify each part from the given circle:


![r=\sqrt[]{43}](https://img.qammunity.org/2023/formulas/mathematics/college/5oo1aox4o2nms7whhramwfn8p1rcppqgh6.png)
With all this, we can say the circle's center is at the point (-2,4) and it has a radius of lenght √43.
Thus, option B is correct.