we know that
the equation of a circle in standard form is
(x-h)²+(y-k)²=r²
(h,k) is the center----------> (3,-1)
r is the radius--------> r=5 units
(x-3)²+(y+1)²=25------> x²-6x+9+y²+2y+1=25---> x²-6x+y²+2y-15=0
the answer is
x 2 - 6x + y 2 + 2y - 15 = 0