Answer:
[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]
Step-by-step explanation:
An ellipse is the locus of a point such that its distances from two fixed points, called foci, have a sum that is equal to a positive constant.
The equation of an ellipse with a center at the origin and the x axis as the minor axis is given by:
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2} =1 \\\\where\ a>b[/tex]
Since the distance of the satellite from the surface of the moon varies from 357 km to 710 km, hence:
b = 357 km + 959 km = 1316 km
a = 710 km + 959 km = 1669 km
Therefore the equation of the ellipse is:
[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]
