So would the equation be

?

I'm still kinda confused on the drawing:

[*]How did you figure the distance of the blue line?

.......
[*]If the diameter of the earth is 8000, then the radius should be 4000, why is there a 4100?

.......That's the distance from the center of the Earth to the satellite at it's minimum height. .......
[*]And what is with the 50, 8300, and 4150?

.......The diameter of Earth + maximum height + minimum height ist the complete major axis of the ellipse. 8000+200+100 = 2a.

**a = 4150**

Since the center of the Earth is a focus the excentricity of the ellipse is 4150 - 4100 = 50

.......

As you may know the ellipse has the property:

I have drawn the minor semi-axis in blue. The slanted line has the length a.