x^2+10x+y^2+16y-k=0
x^2 + 10x + y^2 + 16y = k complete the square on x, y
x^2 + 10x + 25 + y^2 + 16y + 64 = k + 25 + 64
(x + 5)^2 + ( y + 8)^2 = k + 89
To have a circle with a radius of 6, the right side needs to be 36
So
k + 89 = 36
k = 36 - 89 = -53
