Answer
$(x+1)^2+(y+2)^2=(64.6)^2$
Work Step by Step
First of all, we write the equation in standard form as follows:
$x^2+y^2+2x+4y-4091=0$
Now we complete the square for both the variables x and y
$(x^2+2x+1)+(y^2+4y+4)=4091+5$
This simplifies to:
$(x+1)^2+(y+2)^2=(64)^2$
Thus, the center of the Earth is $(-1,-2)$ and the radius is $64$. The weather circles about the center of the Earth but with a radius which is $0.6$ greater than that of the Earth. Now, we can write the equation for the satellite orbit as $(x+1)^2+(y+2)^2=(64.6)^2$