Question 1126986
rewrite the first as 
x^2-6x+y^2+2y=11
complete the square
x^2-6x+9+y^2+2y+1=21
(x-3)^2+(y+1)^2=21
first circle has center at (3, -1) and radius sqrt (21)
The circle concentric with this has center (3, -1) and passes through the origin, since the center of x^2+y^2=16 is a circle with center (0, 0) and radius 4

The radius of the second circle is the distance from the center to the origin, which is sqrt (10).
Its equation is (x-3)^2+(y+1)^2=10  ANSWER
{{{graph(300,300,-10,10,-10,10,-1+sqrt(-(x-3)^2+21),-1-sqrt(-(x-3)^2+21),-1+sqrt(-(x-3)^2+10),-1-sqrt(-(x-3)^2+10),sqrt(-x^2+16),-sqrt(-x^2+16))}}}