Chapter 1.2, Problem 112E

Orbit of a Satellite A satellite is in orbit around the moon. A coordinate plane containing the orbit is set up with the center of the moon at the origin, as shown in the following graph, with distances measured in megameters $\left(Mm\right)$. The equation of the satellite’s orbit is

$\frac{{\left(x-3\right)}^2}{25}+\frac{y^2}{16}=1$

(a) From the graph, determine the closest to and the farthest from the center of the moon that the satellite gets.

(b) There are two points in the orbit with $y$-coordinates $2$. Find the $x$-coordinates of these points, and determine their distances to the center of the moon.