Question

The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 357 km to 710 km. x squared divided by 357 plus y squared divided by 710 equals 1 x squared divided by 1669 squared plus y squared divided by 1316 squared equals 1 x squared divided by 1316 squared plus y squared divided by 1669 squared equals 1 x squared divided by 710 plus y squared divided by 357 equals 1

Answer 1

`(x^2)/(1316^2)+(y^2)/(1669^2)=1`

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:

`(x^2)/(b^2)+(y^2)/(a^2) =1 \\\\where\ a>b`

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:

`(x^2)/(1316^2)+(y^2)/(1669^2)=1`