A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as shown in the figure. The height of the satellite above the earth varies between 110 mi and 440 mi. Assume that the earth is a sphere with radius 3960 mi. Find an equation for the path of the satellite with the origin at the center of the earth. (Assume the elliptical orbit of the satellite lies in the xy coordinate plane with a focus at the origin and the other focus lying on the negative x axis.)