SOLUTION: 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 distance

Algebra ->  Graphs -> SOLUTION: 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 distance      Log On


   

Question 1093744: 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 (Mm). The equation of the satellite's orbit is

+%28x-3%29%5E2%2F25%2By2%2F16=1++
(The first question is to use a graph to find the closest and furthest the orbit is from the center of the moon. The answers to this are
Closest: 2MM
Furthest: 8MM
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. (Round your answers to two decimal places.)

Please help me figure out how to find the x coordinates.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 (Mm). The equation of the satellite's orbit is:
%28x-3%29%5E2%2F25+%2B+y%5E2%2F16+=+1
Convert the equation to y= for graphing
y%5E2%2F16+=+1+-+%28x-3%29%5E2%2F25
multiply by 16
y%5E2+=+16+-+16%28%28x-3%29%5E2%2F25%29
y+=+sqrt%2816+-+%2816%28x-3%29%5E2%29%2F25%29
and
y+=+-sqrt%2816+-+%2816%28x-3%29%5E2%29%29%2F25%29
Graphing these two equations

if the moon is at origin, you can see the furthest and closest is on the x axis at 8 and -2
:
points where y is 2, (blue line) the x value there looks to be -1.4 and +7.4