\text { The point in a lunar orbit nearest the surface of the moon in called perilune and the point farthest from the } \text { surface is called apolune. The Apollo } 11 \text { spacecraft was placed in an elliptical lunar orbit with the perilune } \text { altitude } 110 ~km \text { and apolune altitude } 314 ~km \text { (above the moon). Find the equation of the ellipse if the } \text { radius of the moon is } 1728 ~km \text { and the centre of the moon is at one focus. }