Is my answer correct and how do you know? i just graphed it , is there another way i could do it?

Yes and yes,

the equation of a circle with a center at (h,k) with a radius of "r" is


you know the center (h,k) is (-3,1) and r= 10, so you could plug in the answers and see which ones will match

A more intuitive method of doing it is to recognize that the given equation is like the pythagorean theorem. Also, know that a 3-4-5 is a right triangle and thus a 6-8-10 is also a right triangle.
since radius is 10, that means the other 2 values (x-x1) and (y-y1) must be equal to 6 and 8, so find the answer that will give yuo 6 and 8