The Point in a Lunar Orbit Nearest the Surface of the Moon

Short Answer

The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude $106 \mathrm {~km}$ and apolune altitude $318 \mathrm {~km}$ (above the moon). Find an equation of this ellipse if the radius of the moon is $1728 \mathrm {~km}$ and the center of the moon is at one focus.