Question 1207911
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If you need a refresher on how to complete the square, or why the process works the way it does, check out this page
https://www.mathsisfun.com/algebra/completing-square.html

 
x^2 + y^2 + 2x + 4y - 4091 = 0
(x^2 + 2x) + (y^2 + 4y) - 4091 = 0
(x^2 + 2x + <font color=red>1 - 1</font>) + (y^2 + 4y) - 4091 = 0 .... completing the square for the x terms
(x^2 + 2x + 1) + (y^2 + 4y) - 1 - 4091 = 0
(x+1)^2 + (y^2 + 4y) - 1 - 4091 = 0
(x+1)^2 + (y^2 + 4y + <font color=red>4 - 4</font>) - 1 - 4091 = 0 .... completing the square for the y terms
(x+1)^2 + (y^2 + 4y + 4) - 4 - 1 - 4091 = 0
(x+1)^2 + (y+2)^2 - 4096 = 0
(x+1)^2 + (y+2)^2 = 4096
(x+1)^2 + (y+2)^2 = 64^2


This fits the circle template
(x-h)^2+(y-k)^2 = r^2
where
(h,k) = (-1,-2) = center
r = 64 = radius
I used GeoGebra to verify this. 


The radius 64 is bumped up to 64+0.6 = 64.6 when considering the satellite's orbit.


So,
(x+1)^2 + (y+2)^2 = 64^2
becomes
(x+1)^2 + (y+2)^2 = (64.6)^2
<font color=red>(x+1)^2 + (y+2)^2 = 4173.16</font> represents one possible equation for the satellite's orbit.


If you want you can expand it out to get it into the form Ax^2+By^2+Cx+Dy+E = 0, but I find it's better to keep it as it is.
You'll have to ask your teacher what s/he prefers most.
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