we are given
center=(h,k)=(-16,30)
so, h=-16 and k=30
and it passes through origin (0,0)
so, radius will be distance between (-16,30) and (0,0)
[tex] r=\sqrt{(-16-0)^2+(30-0)^2} [/tex]
[tex] r^2=1156 [/tex]
now, we can use standard equation of circle
[tex] (x-h)^2+(y-k)^2=r^2 [/tex]
we will get
[tex] (x+16)^2+(y-30)^2=1156 [/tex]...........Answer
