Answer
$(x+2)^{2}+(y+8)^{2}=100$
Work Step by Step
An equation of the circle with center $(h,k)$ and
radius $r$ is given as:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Given: center,$(h,k)=(-2,-8)$ and radius, $r=10$
Then
$(x+2)^{2}+(y+8)^{2}=10^{2}$
Hence, $(x+2)^{2}+(y+8)^{2}=100$